A NEW APPROACH TO STOCHASTIC SCHEDULING IN DATA CENTER NETWORKS

International Journal of Computer Networks & Communications (IJCNC) Vol.10, No.5, September 2018
DOI: 10.5121/ijcnc.2018.10501 1
A NEW APPROACH TO STOCHASTIC SCHEDULING
IN DATA CENTER NETWORKS
Tingqiu Tim Yuan, Tao Huang, Cong Xu and Jian Li
Huawei Technologies, China
ABSTRACT
The Quality of Service (QoS) of scheduling between latency-sensitive small data flows (a.k.a. mice) and
throughput-oriented large ones (a.k.a. elephants) has become ever challenging with the proliferation of
cloud-based applications. In light of this mounting problem, this work proposes a novel flow control
scheme, HOLMES (HOListic Mice-Elephants Stochastic), which offers a holistic view of global congestion
awareness as well as a stochastic scheduler of mixed mice-elephants data flows in Data Center Networks
(DCNs). Firstly, we theoretically prove the necessity for partitioning DCN paths into sub-networks using a
stochastic model. Secondly, the HOLMES architecture is proposed, which adaptively partitions the
available DCN paths into low-latency and high-throughput sub-networks via a global congestion-aware
scheduling mechanism. Based on the stochastic power-of-two-choices policy, the HOLMES scheduling
mechanism acquires only a subset of the global congestion information, while achieves close to optimal
load balance on each end-to-end DCN path. We also formally prove the stability of HOLMES flow
scheduling algorithm. Thirdly, extensive simulation validates the effectiveness and dependability of
HOLMES with select DCN topologies. The proposal has been in test in an industrial production
environment. An extensive survey of related work is also presented.
KEYWORDS
Data center network, flow scheduling, network partition, stochastic scheduling model
1. INTRODUCTION
The wide adoption of diverse cloud-based applications and services exacerbates the challenges
the design and operation of Data Center Networks (DCNs). In a multi-tenant mode, long-lasting
elephant and short-lived mouse flows share on DCN paths [15, 46, 60]. According to the results
shown in [7], the sizes of the numerous short-lived flows are usually less than 10KB, and the
average load of these mouse flows is typically less than 5% [7, 45, 46]. However, east-west traffic
in the data center, between 75% and 95%, tends to require very low latency. On the other hand,
the long-lasting heavy DC flows are typically much larger than 100KB; although the number of
these large flows is extremely small compared to that of the small flows [64, 65]. These elephant
flows account for more than 80% of bandwidth in DCNs [45, 102, 110, 112].
To provide high bisection bandwidth, DCN topologies are often multi-rooted topologies, e.g. Fat-
Tree, Leaf-Spine, characterized by a large degree of multipath [40, 41, 96]. There are multiple
routes between any two DCN endpoints [1, 2, 105, 110]. However, a critical issue in such
network topologies is to design an efficient scheduling mechanism to balance the load among
multiple available paths, while satisfying different application requirements defined in the Service
Level Agreements (SLAs).

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The defector DCN flow scheduling scheme Equal Cost Multi-Path (ECMP [3]) cannot meet such
dynamic performance requirements in data centers. Hash collisions in ECMP can cause
congestions, degrading throughput [4-6, 105-107] as well as tail latency [7-9, 109-112] of DCN
flows. To balance the load between DCN switches and paths, stateful schedulers have been
proposed, e.g. Conga [10], Hedera [4], etc. They monitor the congestion state of each path and
direct flows to less congested paths, hence more robust to asymmetry network without control
plane reconfigurations [11, 12]. Since maintaining global congestion information at scale is
challenging, local congestion-aware or stochastic scheduling schemes are proposed, e.g.
Expeditus [12], Drill [13], Hula [14], etc. Using simple or local information collection, these
mechanisms are more efficient and applicable for complex DCN architectures, e.g. 3-tier Clos
topologies. However, the majority of these scheduling mechanisms focus on balancing the loads
of DCN according to the congestion information, without any consideration of cloud applications
or data center traffic patterns.
Existing solutions to scheduling the mice-elephants hybrid DCN traffic fall into two categories.
The first category deploys unified schedulers for both mice and elephants on shared paths, in spite
of the competing performance requirements of the two. Based on the analysis of DC traffic
patterns, these studies design novel scheduling algorithms or congestion signals [16, 17] and
strike at the right balance between throughput and latency on shared DCN paths. The main
challenge though is the interference between the elephant and mouse flows. The second category
deploys network partition schemes that transfer the two types of flows over separate paths. [18,
60-63, 100, 101, 103, 104] By isolating elephant and mouse flows, network partition solutions
avoid the aforementioned interference. This is particularly attractive as hardware and system cost
continues to drop. Nonetheless, new policies are required to adaptively partition the DCN paths,
given dynamic DC traffic patterns and varied DC architectures.
This paper focuses on the second category, the network partition solutions. Using a stochastic
performance model, we first theoretically prove that the interference between mice and elephants
are inevitable under the unified scheduling mechanism, indicating that network partition is a more
appropriate solution for handling such hybrid DC traffic. We then propose a novel scheduling

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scheme, HOLMES, for such hybrid traffic in data centers. HOLMES architecture partitions a
DCN into high-throughput and low-latency sub-networks, decouples the two competing scenarios
and eliminates the interference in the hybrid traffic. HOLMES further deploys a stochastic and
global congestion-aware load balancing algorithm that optimizes the performance of each sub-
network. The stability of the HOLMES flow scheduling algorithm is also proved and validated in
this paper.
Fig. 1. HOLMES architecture: Based on the real-time monitor information, HOLMES AI module
first analyzes the status or tendency of the DCN using machine learning models, and generates
the learning results. Next, according to the analysis results, HOLMES control layer designs a
network partition policy and a corresponding flow scheduling policy, and the policies are
generated in the SDN controllers. Finally, the network partition as well as the flow scheduling
operations will be executed on the DCN switches or hosts, under the guidance of the SDN
controllers.
2. HOLMES ARCHITECTURE
Fig. 1 shows the HOLMES architecture in three layers: AI layer, control layer and the
infrastructure layer. The HOLMES AI layer contains a cognitive computing cluster to implement
the software AI module. The AI module collects the DCN state information from the DCN
monitors, and applies the machine learning algorithms to generate some analysis results, e.g.
networking tendency predictions, network outlier locations, etc. These learning results generated
by the AI module provide a more comprehensive view of DCN behaviors. They will be then used
for network partition and flow scheduling operations.
The HOLMES control layer is responsible for generating the network partition, congestion
control, and local balancing policies, based on the monitoring information as well as the learning
results generated by the AI module. The policies generated in the SDN are decomposed into a
series of fine-grained partition and scheduling orders, which are transmitted to the DCN switches
and end hosts for execution. Without deploying the HOLMES AI module, the functions provided
by the control layer are the same as the traditional SDN controllers.

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The HOLMES infrastructure layer executes the specific network partition as well as the flow
scheduling operations. It is responsible for storing, forwarding and processing data packets. The
detailed operation orders are transmitted and configured on the DCN switches. The DCN
switches the first map each link to the high throughput network or the low latency sub-network,
according to the network partition policies. When the elephant and mouse flow to arrive at a DCN
switch, their packets are scheduled to the pre-partitioned paths separately. This process is
managed by the HOLMES control layer.
A. Application Scenarios for HOLMES Architecture
Compared with the commonly used SDN architectures, a prominent feature of HOLMES is the
implementation of the AI module and its machine learning algorithms. Machine learning methods
have been widely used in network management [72-74, 95] and DC scheduling policy generation
[75, 76, 96] operations. Those continuing learning and analysis results provide a comprehensive
understanding of network features and behaviors, which benefits the designing of the
corresponding network partition and flow scheduling policies. Therefore, the deep analysis and
accurate AI prediction provided by the AI module enable the HOLMES architecture to perform
more complex and intelligent operations.
One typical application scenario for HOLMES architecture is the deployment of application
driven-networks (ADN) [77], where a physical network is sliced into logically isolated sub-
networks to serve different types of applications. Each network slice in ADN can deploy its own
architecture and corresponding protocols, to satisfy the requirements of the applications it serves.
The key operations when implementing ADN are: (1) Constructing an application abstraction
model to formulate the resource requirements of the applications; (2) mapping the distinct
properties of applications to respective network resources. It is shown that the complexity and
performance of these operations can be improved when some application features are pre-known
[8]. Hence, the HOLMES AI module benefits the analysis of application features as well as the
prediction of resource requirements, which further alleviate the complexity of application
abstractions and mapping operations. Moreover, the design and implementation of network
slicing mechanisms can also be realized by the cooperation of the control layer and the
infrastructure layer.
Similarly, HOLMES architecture is also applicable for some other intelligent or complex
application scenarios, which demand a deep understanding of network or application features
such as Internet of Vehicles (IoV) [78], co flow scheduling [79, 80] and some other network
architecture based on network slicing or network partitions. With the immense proliferation of
complex and diverse cloud-based applications, we expect such architecture to be the development
trend in the future.
B. Out-of-order vs. Efficiency
While elephants contribute to the majority volume of DCN traffic, mice account for 80% of the
number of instances. [45, 102] Out-of-order scheduling done at host side may sacrifice efficiency.
In addition, compatibility with legacy hardware has to be ensured. Therefore, one may still
consider deploy conventional, sometimes oblivious, ECMP scheduling for in-order scheduling of
mice.

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3. HOLMES SCHEDULING ALGORITHMS
Once the hybrid DC traffic is separated into different sub-networks, scheduling algorithms affect
the performance of each sub-network. In this section, we discuss the aforementioned global
congestion-aware scheduling algorithm and prove the stability of its stochastic policy.
A. Deploying Stochastic Scheduling Algorithms
Compared with the other state-aware flow scheduling algorithms, stochastic flow scheduling
algorithms are more applicable for large-scale data centers according to the following reasons:
1. Simplification of computing complexity
One of the key factors that degrade the performance of the traditional ECMP mechanism is the
lack of global congestion information. To overcome this limitation, a group of studies has
designed new flow scheduling policies based on a global “macroscopic” view of the entire DCN,
e.g. CONGA [10]. However, in large-scale and heavily loaded data centers, the global
macroscopic load balancing algorithms introduce unacceptable computing complexity to deal
with the massive information, and the control loops in these scenarios are much slower than the
duration of the majority of congestion incidents in data centers [13]. Therefore deploying the
stochastic algorithms to achieve micro load balancing is a more viable solution. The micro load
balancing solutions require only limited congestion information, which simplifies the computing
complexity and enables instant reactions to load variations in large-scale data centers.
2. Optimization of storage complexity
In data centers, 8 and 16-way multipathing are common, while there is growing interest in
multipathing as high as 32 or even 64. Specifically, with 40 servers in a rack, there will be 40
uplinks. Each flow can use a different subset of the 40 links, leading to 240
possible subsets.
Keeping the state of each path in this scenario requires unacceptable storage resources, which is
difficult to be implemented. On the contrary, stochastic scheduling algorithms are effective to
cope with the optimization of storage complexity, as well as the small number of register reads.
Edsall et al [26] deploy the stochastic power-of-two-choices hashing solution for balancing loads
of DC routers. The storage complexity of such a stochastic solution is logarithmically reduced.
3. Better adaptability for heterogeneous DCNs
A typical flow scheduling method in multi-rooted DCNs is equal traffic splitting based on
hashing, as used in the traditional ECMP approach. However, the uniform hashing approach
cannot achieve optimal load balance without the assumption of symmetric and fault-free topology
[5, 10, 45, 46], which is not generally true in heterogeneous data centers. To provide better
adaptability for heterogeneous DCNs, weighted traffic distribution methods have been widely
adopted in the global macro load balancing solutions [11, 67]. In order to correct the imbalance
caused by the even distribution approach and enable fair resource allocation, the weighted
approaches distribute the traffic among available paths in proportion to the available link capacity
of each path. The global weighted traffic distribution solutions have shown good adaptability to
dynamically changing network topologies. However, these solutions still need real-time state
information collection of all the paths, which introduces additional computing and storage
complexity.

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Stochastic flow scheduling algorithms can reduce the computing and storage overhead of
weighted traffic distribution mechanisms, while maintaining the adaptability to heterogeneous
DCN topologies. Consider the stochastic Power-of-Two-Choices: The algorithm only needs to
record the states of the two randomly chosen paths; therefore, the storage and computing
complexity are dramatically reduced. Moreover, the algorithm compares the load conditions of
these two chosen paths, select the better one, hence performs a weighted operation in another
form. Stochastic load balancing solutions have also been proved to be applicable for
heterogeneous DCNs [13, 26]. Based on these justifications, we extend stochastic flow scheduling
algorithms to our HOLMES mechanism.
B. Flow Scheduling Algorithm in HOLMES
We consider a stochastic scheduling policy, (d, m) policy: The input port chooses d random end-
to-end paths out of all the possible paths. It finds the path with the minimum occupancy among
all the d samples and m least loaded samples from the previous time slot. It then schedules the
input packet to the selected end-to-end path.
Increasing the value of d and m to >>2 and >>1 will degrade the performance since a large
number of random samples makes it more likely to cause the burst of packet arrivals on the same
path [13]. As a result, we set m=1 and d=2 in our scheduling model. The detailed flow scheduling
procedure is shown in Alg. 1.
Using global congestion information, the algorithm reacts rapidly to the link or node failures.
Moreover, the limited information used in the algorithm improves the scheduling efficiency while
avoids the traffic bursts on the same switch ports.
Algorithm 1 Flow scheduling policy in HOLMES
1: Input: Load condition of each end-to-end path at time
t:
{load(1), load(2), load(3),…}
Path number of the selected path at time t -1:
s(t-1)
Output ports of the TOR and aggregate
switches on each path:
(1) (1) (2) (2){{ , },{ , },...}A T A T
P P P P
2: Output: Path number of the selected path at time t -1:
s
Output ports TOR and aggregate ports on the
selected path:
( ) ( ){ , }A T
s sP P
3: Initialize: m = 2, d = 1;
4: Initialize: loadOPT = load(s(t-1)
);
5: Random select m end-to-end paths {Path(1),
Path(2), …, Path(m)}
6: Construct candidate set: L ←{Path(1), Path(2), …,
Path(m)}∪{s(t-1)
}
7: for each path i (1 ≤ i ≤ m+1) in the candidate set L do
8: if load(Path(i)) ≤≤≤≤loadOPT then
9: loadOPT = load(Path(i));
10: end for
11: Assign value: s = Path number of the path with
load loadOPT:
12: return { pA
(s), pT(s) } and s

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C. Stability Analysis of HOLMES’s Scheduling Algorithm
We prove the stability of this stochastic global congestion-aware scheduling algorithm in a two-
tier Clos DCN topology. We abstract an end-to-end path in a Clos network (Fig. 2A) as a serial
queuing system consists of a series of queues (Fig. 2B). As a result, the whole Clos DCN
topology is abstracted as a queuing network. We then evaluate the performance of a specific leaf-
to-spine DCN path using a stochastic queuing network model.
We focus on analyzing the stability of the scheduling process from when a packet arrives at a
TOR switch to when the packet reaches the spine switch. The packet experiences two queuing
processes, at the TOR and the aggregate switch port, respectively. The entire path from the TOR
node to the spine node can also be modelled as a large queue.
Based on the results of [53-56] and with a similar method shown in [57-59], we prove that
HOLMES’s scheduling algorithm is stable for all uniform and non-uniform independent packet
arrivals. Some key notations and definitions used in the scheduling model are illustrated in Table
II.
Fig. 2. Abstraction of a leaf-to-spine path in a Close network (A) to a serial queuing system (B)
We prove that the global (1, 1) policy is stable for all admissible parallel arrival process. We
construct a Lyapunov function L as follows:
* 2 2
1 1
( ) ( ( ) ( )) ( )
A ANN NN
i i
i i
L t Q t Q t Q t
= =
= − +∑ ∑%
To prove the algorithm is stable, we show that there is a negative expected single-step drift in the
Lyapnuov function, i.e.,
[ ( 1) ( ) | ( )] ( ) ( , 0)E L t L t L t L t k kε ε+ − ≤ + >

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We divide the Lyapunov function into two sub functions as:
* 2
1
1
( ) ( ( ) ( ))
ANN
i
i
L t Q t Q t
=
= −∑ % 2
2
1
( ) ( )
ANN
i
i
L t Q t
=
= ∑
Based on the above formulation, we prove that there exists a negative expected single-step drift in
the Lyapnuov function in each possible case. Therefore, the global (1, 1) policy is stable. Based
on the (d, m) policy, the HOLMES’s scheduling algorithm is also stable. Please see details of the
proof in Appendix B.
4. HOLMES PERFORMANCE EVALUATION
We evaluate HOLMES using simulation based on OMNET++ [99]. We construct a test-bed
simulation platform to simulate the data transmission process in symmetric and asymmetric fat-
tree DCNs. Similar to [10, 46, 52, 60, 62, 63], a heavy-tailed distribution is used to generate DC
flow of different sizes. The hosts of the DCN run TCP applications. The flow request rate of each
TCP connection satisfies the Poisson process.
A. Evaluation of HOLMES Network Partition
We evaluate the network partition policy of HOLMES in a scenario that hybrid elephant and
mouse flows are scheduled in the same DCN with different scheduling schemes. The DCN
topology deployed in this experiment is a Clos network with 2 and 4 leaf and spine switches
respectively. We generate elephant and mouse flows to leaf switches with average sizes of 100KB
and 1KB, respectively. The queue lengths of the switch ports are used as performance indicators.

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Since the scale of the DCN in the simulation is not very large, HOLMES deploys the static policy
that partitions the two sub-networks in advance. The buffer sizes of all the switch ports are set to
be the same. When the buffer of a switch port is full, all the upcoming input packets to that port
will be dropped. We compare HOLMES against two start-of-the-art unified load balancing
schemes: CONGA [10] and queue length gradient based scheduling. Similar to the delay gradient
based congestion control policy used in [16, 66], we deploy the queue length gradient as the
indicator and schedule the arrived packet to the port with the minimum length gradient.
Figs. 3A-3C show the queue length variation of the four ports of a spine switch under the three
scheduling schemes. The X-axis indicates the time period and the Y-axis denotes the queue length.
We can see from Fig. 3A that using CONGA, the buffers of all the four ports are full after a
period of time, indicating the throughput of the switch has been maximized, which benefits the
transmission of the elephant flows. However, when a mouse flow arrives, all the packets in that
flow have to wait for a long queuing time since all the output port are of heavy loads.
Consequently, the latency of the mouse flow will increase and degrade the overall performance of
the hybrid DC flows.
Similarly, as shown in Fig. 3B, the buffers of the four output ports are also almost full after a
period of time using the length gradient based policy. The results indicate that the length gradient
based load balancing policy still suffers from the interference between the elephant flows and the
mouse flows.

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Fig. 3. Queue length changing trends of a DCN spine node’s ports under policies CONGA (A), length
gradient based policy (B) and HOLMES (C)
Comparing Fig. 3A and Fig. 3B, we find that the load balancing condition of the gradient-based
scheme is a little worse than CONGA. The reason is that the gradient-based scheme schedules the
DC flow according to the changing trend but not the current state of the DCN. Finally, Fig. 3C
shows that HOLMES has successfully isolated the elephant and mouse flows. Two of the ports
have been partitioned to the low latency sub-network and used for transmitting the mouse flows.
Fig. 3C shows that the buffers of the two ports are almost empty during the entire transmission
procedure. Thus, packets in the mouse flows do not need to wait for additional queuing delays,
and the low latency of the mouse flow is ensured. Moreover, the buffers of the other high
throughput ports are also full filled, which satisfies the throughput requirements of elephant flows.
Hence, by isolating the mixed traffic, HOLMES network partition policy successfully eliminated
the interference of the elephant flows to the mouse flows.
The main shortcoming of the network partition solution is the inefficient use of network resources.
Although the isolation of the hybrid traffic avoids the interactions of the elephant and mouse
flows, the spared network resource in the low latency paths has not been fully used since the
buffers of these paths are almost empty. An effective solution is to improve the buffer allocation
by limiting the buffer size of the low latency sub-network and assigning the spared buffers to the
high throughput sub-network. This policy has been implemented in [61].
B. Stability Validation of HOLMES Scheduling Algorithm
We evaluate the stability of HOLMES flow scheduling algorithm. We simulate the scenario that
DC traffic are scheduled in a DC with asymmetric network topology. We combine two different
sized Clos networks, and construct an asymmetric DCN architecture. One of the Clos network
consists of 2 leaf switches and 4 spine switches. The other is a Clos network with 5 and 4 leaf and
spine switches, respectively. 10 hosts are attached to each leaf switch. We concentrate on
validating the stability of HOLMES flow scheduling algorithm, rather than the network partition
mechanism in this scenario. Thus, we do not deploy the HOLMES network partition mechanism
in the experiment and only execute the HOLMES flow scheduling algorithm.
CONGA [10] and DRILL [13] are two load balancing solutions proven to be stable. Therefore,
we compare them against HOLMES. All DC traffic is scheduled with the granularity of packet,
and we focus on analyzing the stability of the three scheduling algorithms. When using the Power
of Two Choices selections, we uniformly set d=2 and m=1. Similarly to the previous experiments,
we deploy queue length as the load balance indicator to evaluate the overall load balancing
condition of the DCN.

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Figs. 4A-4C show the queue length changing trend of a specific leaf switch’s ports, under load
balancing policies CONGA, DRILL and HOLMES. We can see from Fig. 4A that the queue
length changing trends of all the ports in a leaf switch are almost overlapped under CONGA,
indicating that the queue lengths of all the switch ports are almost the same at each time unit.
Therefore, the load balancing condition under CONGA is optimal among all the three
mechanisms, since CONGA makes each scheduling decision based on the global congestion
information. Without considering the time used for obtaining congestion information, CONGA
obtains the global optimal load balancing result.
Fig. 4B shows the queue length changing trends of the same leaf switch ports under DRILL.
Different with the former results, we find fluctuations in the queue length changing curve. In
other words, the length difference of the longest queue and the shortest queue is clear. The reason
is that the use of (d, m) policy in DRILL reduces the scale of the solution space, and the local
optimal solutions affect the load balancing condition of the DCN.
Fig. 4. Queue length changing trends of a DCN leaf node’s ports under load balancing policies CONGA
(A), DRILL (B) and HOLMES (C)

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Fig. 4C shows the queue length changing trends of the same leaf switch ports under HOLMES
scheduling algorithm. The fluctuations also exist in the curve of Fig. 4C, where the amplitude of
the fluctuation is more obvious. This phenomenon is also caused by the use of (d, m) policy.
Compared with DRILL, the global (d, m) policy used in HOLMES further limits the solution
space, and exacerbates the fluctuations. However, although the fluctuations are more obvious
when executing HOLMES flow scheduling algorithm, we can also find an upper bound (about 10
packets) of the fluctuation amplitude, indicating that the length difference of the shortest and the
longest queue is not infinite in HOLMES. Hence, our HOLMES flow scheduling algorithm is
stable during the whole scheduling period. Moreover, limiting the solution exploration space
reduces the time used to obtain the congestion information and make HOLMES more efficient
and applicable for large-scale data centers.
C. Adaptability for Heterogeneous
As discussed earlier, both the stochastic flow scheduling algorithm and the weighted traffic
splitting solutions can adapt to heterogeneous congestion states. We now evaluate the adaptability
of the two solutions.
We first theoretically compare the approximate adaptability of the two solutions, as shown a
simple leaf-spine DCN topology with N paths available between two racks as shown in Fig. 5.
Fig. 5. Simple leaf-spine DCN topology for adaptability evaluations
We show that when the load conditions of the DC paths are heavily heterogeneous, the (d, m)
policy also needs to maintain plenty of load status information to keep its adaptability as good as
the weighted traffic splitting solutions. The stochastic scheduling mechanism does not show
obvious advantages in this scenario.
Similar to the experiment in [97], we simulate the execution process of the coordinate approach
as well as the Power-of-Two-Choices algorithm on a same switch. Fig. 6 shows the changing
trend of the overall switch load as the modeling factor (d) increases.
The load distribution of the switch ports is initialized exponentially in this experiment. We see
from Fig. 6 that, as the value of d increases, the load condition of the switch is improved under
the power of two choices policy ((d, m) policy); since a larger value of d increases the probability
of choosing the lightest loaded output port. As we increase the value of d from 2 to 5, the power
of two choices policy performs almost as well as the theoretical load optimal policy (d = 10),
which validates our previous modeling results. On the contrary, when using the coordinated

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approach, the switch attains optimal performance when the value of d is small (d = 2) and the load
state of the switch is almost as good as the theoretical load optimal policy. This simulation result
is in accordance with the analysis in [97]. However, as the value of d increases, the load state of
the switch becomes worse: when assigning d = 10, the load balancing condition of the switch
under the coordinated policy is even worse than the (2, 1) policy.
Although the stochastic flow scheduling outperforms the weighted traffic splitting solution in
most cases, it still has some limitations. The weighted traffic splitting solution maintains the load
status of all the paths. It dynamically adjusts the value of each weight according to the current
load status of each path (the static weight configuration has proven to be not applicable in [10]).
However, when deploying the (d, m) policy, the value of d and m are constant after the
initializations. Thus, when the values are not appropriately assigned, (d, m) policy will not
perform as well as the weighted traffic splitting solutions. Hence, the HOLMES AI module is
responsible for analyzing the overall heterogeneity degree of a DCN, and guiding the flow
scheduling algorithm to set appropriate values of the algorithm factors (d and m). The detailed
design and implementation of the HOLMES AI module is our future work.
D. Technical Challenges in Hardware Implementations
Some technical challenges need to be considered to implement HOLMES in real-world data
centers. We now summarize these challenges in hardware implementations.
1. Handling the packet reordering
The flow scheduling algorithm in HOLMES can be implemented with different data granularities:
per packet scheduling, per flow scheduling or some intermediate data sizes, e.g. flow cell [24],
flow let [10], etc. When using the TCP transmission protocol and implementing the per packet (or
flow cell) scheduling, some studies have shown that this fine-grained traffic splitting techniques
cause packet reordering and lead to severe TCP throughput degradations [23]. Therefore, the
packet reordering problem needs to be considered when implementing the fine-grained HOLMES
traffic scheduling algorithm. A viable solution is to deploy the JUGGLER [68] network stack in
data center traffic transmissions. JUGGLER exploits the small packet delays in datacenter
networks and the inherent traffic bursts to eliminate the negative effects of packet reordering
while keeping state for only a small number of flows at any given time. This practical reordering
network stack is lightweight and can handle the packet reordering efficiently.
Fig. 6. Changing trend of a switch’s overall traffic load under different policies

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2. Design of DCN forwarding and state tables
The design of the forwarding and state tables is also a noteworthy challenge. An appropriate
approach should cope with the small time budget as well as the small register usage. We now
propose a viable design to implement the per-flow scheduling algorithms of HOLMES.
As shown in Fig. 7, a TOR switch maintains a flow table and a state table. The two tables work
together to execute the load balancing policy attained from the SDN controller. Specifically,
when a packet arrives, its flow ID is hashed to map the packet to a flow table entry. If the table
entry is valid, the packet is dispatched to the path indicated by the stored hash applied to the
packet’s flow ID. On the contrary, if the packet’s flow ID is not maintained in the flow table, the
TOR switch will look up the destination TOR ID in the state table. After that, the (d, m) policy is
applied to compare the load states of the three candidate end-to-end paths to the destination TOR
(r1_metric, r2 metric and r3_metric), and assign the packet to the optimal path. Two of the three
end-to-end paths are randomly selected. The third one is the optimal path from the last selection.
Finally, the flow ID and the hash of the chosen path will be inserted into the flow table.
{
Fig. 7. Overview of HOLMES forwarding and state tables: A new flow table entry is set up by applying
the (2, 1) policy in the state table. The period timer of each table is triggered every time period T1 and T2 to
age out inactive flows and update the load status of each candidate end-to-end path.
The information of each table needs to be updated periodically to keep the real-time status of the
traffic and paths. Thus, we associate an aging bit with each table entry. The aging bit of the flow
table is responsible for marking inactive or idle flows: when a packet’s flow ID maps the
information in the forwarding table, the aging bit is cleared to indicate that the flow entry is active.
A timer process visits every table entry every aging timeout T1. When the timer process visits a
table entry, it either turns on the aging bit or invalidates the entry if the aging bit is already on. In
other words, T1 is the timeout threshold to age out inactive flows, which is proportional to the size
of the scheduling unit e.g. per-flow, per-flow cell, etc. If the packet’s flow ID is not maintained in
the flow table, the TOR switch will execute the (d, m) policy on the state table. Thus, T1 can also

15
be considered as the time period to trigger the execution of the HOLMES scheduling algorithm.
On the other hand, another timer process runs together with the aging bit of the state table to
update the load status of each candidate end-to-end path. The timeout threshold to age out the old
status information in the state table is set to T2. To ensure that the latest load state information is
used when executing the (d, m) policy, the value of T1 and T2 should satisfy: T1 ≥ T2. Moreover, in
most cases, the global congestion control signals deployed in the flow scheduling algorithms are
the feedback signals from the receivers of the end-to-end paths. Thus, we further get: T1 ≥ T2 ≥
RTT. Key et al [93] have suggested that the policy that periodically sampling a random path and
retaining the best paths may perform well.
The periodically sampling of path congestion states in the state table makes the real-time
collection of status information becomes a technical challenge. The state collection operations
should not introduce obvious transmission overheads and performance penalties. Especially in the
TCP in cast scenarios [69, 70] where multiple source nodes transmit traffic at the same time to a
common destination node, the state collection operations introduce additional traffic and are
prone to cause DCN throughput collapse [71]. A viable solution for collecting the real-time
congestion status is deploying RepSYN as the signal to detect the load conditions of the multiple
paths, as shown in [33]: before transmitting data among multi-rooted paths, multiple TCP
connections are established; however, traffic is only transmitted using the first established
connection and the other connections are ended immediately. The delay experienced by an SYN
reflects the latest congestion condition of the corresponding path, and thus the congestion states
can be collected. Moreover, this solution only replicates SYN packets to probe the network,
which does not aggravate the TCP in cast in a DCN.
The state table only needs to periodically maintain the congestion states of two randomly chosen
paths and the congestion-optimal path in the latest time unit. Compared with some other
congestion-aware solutions e.g., CONGA [10], RepFlow [32], the storage complexity has been
dramatically optimized. In order to make the scheduling results of the (d, m) policy more effective,
we choose the disjoint end-to-end paths (paths with different intermediate aggregate or spine
switches) to avoid the scenario that the same local congestions is shared by multiple end-to-end
paths. This implementation is applicable for more complex multi-tier Leaf-Spine topologies or
asymmetric DCN topologies.
3. Dealing with the stale information
When implementing HOLMES scheduling algorithm with packet granularity, the transmission
latency of a packet is so small that the information refresh rate in the state table cannot catch up
with. Correspondingly, the load balancing algorithm has to use the stale information to make the
scheduling decisions [94, 98] have pointed out that the delayed information leads to a herd
behavior of the scheduling results: data will herd toward a previously light loaded path for much
longer time than it takes to fulfill the path. Thus, another technical challenge is to deal with the
stale information used in the load balancing algorithms. (More detail including Figure 8 is
omitted due to limited space allowed.)
Overall, the simulation experimental results validate the modeling results. They show that
HOLMES load balancing algorithm is stable and adaptable in heterogeneous DCNs.
5. RELATED WORK
Latency and throughput optimization for DCN has attracted increasing attention. A series of
solutions have proposed to improve the performance of the scale-out multipath data center
topologies, such as Clos networks [1, 2, 19], Flattened Butterfly [20], HyperX [21], DragonFly
[22], etc. In general, the performance optimization mechanisms can be classified into two
categories: temporal solutions (i.e. congestion control mechanisms) and spatial solutions (i.e. load
balancing mechanisms). Specifically, one can classify the existing solutions according to Fig. 9.

16
A. Congestion Control Mechanisms – Temporal Solutions
DC congestion control is a deep studied topic. Generally, the congestion control mechanisms
adjust the traffic transmission rates or the packet dropping strategies according to the feedback
congestion signals. The control mechanisms can be implemented on either the end hosts or the in-
network equipments.
1) Host-based congestion control mechanisms
The optimization of the transport protocols are usually host-based solutions. Those newly
proposed transport protocols are customized for DCNs. The host-based control mechanisms can
be implemented on either the sender [7, 16] or the receiver of a transportation path [87]. Jain et al
[88] study the general patterns of response time and throughput of a network as the network load
increases. They describe the changing trend of network performance curve using two factors: cliff
point and knee point. As shown in Fig. 2 of [88], the point of congestion collapse is defined as a
cliff due to the fact that the throughput falls after this point (packets start getting lost); and the
point after which the increase in throughput is small (buffers of a path start to be filled) is
described as a knee point. Correspondingly, the host-based congestion control policies can also be
categorized using the two factors.
Fig. 9. Classification of DCN congestion control and load balancing mechanisms; the design space for
HOLMES flow scheduling algorithm
Cliff-based mechanisms: Most of the modified transportation protocols based on the traditional
TCP protocol are cliff-based mechanisms, such as MPTCP [89], DCTCP [7], D2TCP [90], etc.
The cliff-based mechanisms are loss-based solutions, which interpret packet losses as congestions
and attempt to fulfill the buffers of the TCP paths while avoiding the occurrence of packet losses
[66]. These solutions deploy different types of feedback information from the last time point as
the congestion signals to guide the traffic control in current time point. For example, DCQCN [49]
combines Explicit Congestion Notification (ECN [7]) markings with a QCN [50, 53-55] inspired
rate-based congestion based control algorithm to control DCN flows. The cliff-based mechanisms
are usually the throughput-optimal solutions.

17
Knee-based mechanisms: Cardwell et al [91] point out that the operating point of the cliff-based
mechanisms is not optimal. They argue that when the scale of a DCN is large enough, there will
be quantities of packets accumulated in the buffers of a path. Thus, compared with the data
transmission time in the network links, the queuing time in the buffers tend to dominate the
overall data transmission latency. Thus, the cliff-based solutions are not applicable for the
optimization of the data transmission latency. Furthermore, they propose a novel congestion
control mechanism BBR, which adjust the operating point from the cliff point to the knee point,
to optimize the data transmission latency of a DCN. Therefore, the cliff-based congestion control
mechanisms are usually the latency-optimal solutions.
In-between: Different with the above two types of solutions that optimize the throughput or
latency of a DCN respectively, a few mechanisms focus on handling the trade-off between
latency and throughput, and attempt to find the right balance of the two conflicting factors.
Hayes et al [17] propose a delay gradient algorithm for TCP congestion control of wide-area
networks. Similarly, taking inspiration from Compound [47] and FAST [48], TIMELY [16] also
deploys delay gradient as the congestion signal and proposes a gradient-based algorithm to jointly
optimize the latency and throughput of a DCN in different time periods. TIMELY mechanism
works during the time period between the knee and cliff points, which dynamically adjusts the
importance of the throughput and latency issues.
2) In-network congestion control mechanisms
Network congestion usually occurs in the in-network devices, e.g. switches and routers. Thus,
compared with the end host based solutions, the in-network congestion control mechanisms
achieve more accurate congestion information and react more quickly to congestions and failures.
Taking this advantage into account, many researchers migrate some status monitoring and flow
control functions from end hosts to in-network devices. Correspondingly, a series of in-network
congestion control mechanisms have been proposed.
Most of the in-network congestion control protocols adjust the congestion window size by
managing the queues of the DCN routers. Quantities of Active Queue Management (AQM)
algorithms have been proposed to generate congestion signals according to the real-time queue
lengths in DCN routers, such as Adaptive RED [81, 82], Adaptive Virtual Queue (AVQ) [83],
BLUE [84], etc. Hollot et al [85] apply classical control system techniques to design novel
controllers that are better suited for AQM. Similarly, Firoiu et al [86] model the AQM RED
algorithm as a feedback control system and discover fundamental laws governing the traffic
dynamics in TCP/IP networks. pFrabic [51] preemptively schedules flows using packet
forwarding priorities in switches and Detail [9] deploys a similar mechanism that give priorities
to latency-sensitive mouse flows; however this simple control mechanism makes a mismatch
between injection traffic and network capacity, results in packet loss and bandwidth wastage.
These in-network solutions react quickly to the real-time congestions and failures; moreover, they
can also generate feedback congestion signals to the end hosts, and cooperate with the host-based
control mechanisms.
B. Load Balancing Schemes – Spatial Solutions
Different with the congestion control mechanisms, the load balancing schemes try to improve the
DCN performance from a spatial aspect. This kind of solutions is especially applicable for the
traditional multipath DCN topologies.
Similarly to the traditional traffic engineering techniques, some studies deploy the centralized
scheme to schedule the DC traffic. SWAN [27] and B4 [28] collect statistical information from

18
switches to a central controller, and push forwarding rules to balance the load for inter-datacenter
WANs. Fastpass [42] deploys a centralized scheduling algorithm to ensure that the queues stay
small while the queuing delay remains near optimal. Hedera [4] and MicroTE [29] also apply the
centralized scheduling scheme and focus on the load balancing across multiple DC paths.
The main shortcoming of these centralized solutions is that they suffer from high control-loop
latency in large-scale data centers, which are not applicable for handling highly volatile DC
traffic in time [14]. Addressing this issue, quantities of scalable distributed load balancing
schemes have been proposed. One can further categorize these solutions as stateless solutions and
congestion-aware solutions.
Fig. 10. Correlations between the DCN congestion controller and load balancer in a control theoretic
model
1) Stateless load balancing schemes
ECMP [3] is a simple hash-based load balancing scheme that is widely used as the de facto
scheme in switch ASICs today. The coarse-grained per-flow load balancing and the congestion
agnostic hash collisions in ECMP have shown to cause performance degradation in asymmetric
DCN topologies [10, 25, 26], during link failures.
To overcome the above-mentioned shortcomings in ECMP, quantities of solutions have been
proposed to improve the traffic splitting granularity or the load balancing algorithm. PLTS [23]
and DRB [5] is per-packet load balancing schemes that schedule DC traffic with the granularity
of the packet. Presto [24] splits traffic into 64KB sized TSO (TCP Segment Offload) segments.
Round robin fashion [6] is deployed in DRB and Presto to spray DC packets or flow cells. Based
on Valiant Load Balancing (VLB [37]), some other solutions have been put forwarded to improve
the failure tolerance of homogeneous and heterogeneous network topologies [38, 39].
None of the above solutions are state-aware, which causes performance degradation during link
failures.
2) Congestion-ware load balancing schemes
The main drawback of the stateless schemes is causing performance degradation during link
failures. Addressing this issue, a series of congestion-aware load balancing schemes have been
proposed. Based on global or local congestion information, the congestion-aware solutions are
more applicable for asymmetric topologies or link/switch failure scenarios.
Global congestion aware schemes: Global congestion-aware load balancing schemes deploy the
end-to-end congestion signal as the feedback metric to schedule the DC traffic among multiple
paths. TexXCP [30] and MATE [31] are adaptive traffic-engineering proposals that balance the
load across multiple ingress-egress paths in the wide-area network, using the per-path congestion
statistics. CONGA [10] proposes similar solutions for datacenters, by spraying DC traffic among

19
multi-rooted networks based on the congestion state of each end-to-end DC path. RepFlow [32]
and RepNet [33] replicate each mouse flow to opportunistically use the less congested path, and
reduce the overall flow completion time in DCNs. Inspired by the Minimum Delay Routing [34],
HALO [35] studies load-sensitive adaptive routing and implements its solution in the router
software. These solutions are aware of the overall congestion status of the DCN and react fast for
local failures or congestions.
Local congestion aware schemes: Using the global congestion-ware schemes to make load
balancing decisions faces scalability challenges. Although the distributed architecture can
improve the scalability of the scheduling schemes, they require coordination between switches or
hosts. In large-scale data centers with high transmission rates, the continuously reacts to each
congestion information introduce additional latencies and degrade the overall flow scheduling
performance [13]. Consequently, the local congestion-aware solutions have drawn large interests.
Local Flow [25] and Flare [36] study the switch-local solutions that balance the load on switch
ports, without taking the global congestion information into account. Based on the Power-of-
Two-Choices model [43, 44], Ghorbani et al [13] propose a stochastic switch-local scheduling
scheme that further reduces the polling range of local solutions, and improves the execution rate
of the flow scheduling algorithm.
As an improvement of CONGA[10], HULA [14] tracks the next hop for the best path and its
corresponding utilization for a given destination, instead of maintaining per-path utilization
congestion information. This novel strategy makes the load balancing scheme applicable for more
complex DCN topologies, besides the two-tier Leaf-Spine topologies. Based on limited
congestion information, the local congestion-aware solutions provide suboptimal routing
decisions, while improve the overall policy execution rate. However, the stability and
convergence of these switch-local solutions need to be ensured; worse more, as aforementioned,
the local congestion-ware scheduling policies have been proved to react slowly to link failures
[10, 14] and are prone to form congestion trees.
The implementation of the deterministic congestion-aware load balancing schemes requires
recording the real-time load status of all the available paths or links, to make the global or local
optimal choices. As previously discussed in Section V, keeping the status information and
calculating the optimal solution in large-scale datacenters introduce unacceptable storage and
computing complexity. Taking inspiration from this issue, we deploy a probabilistic global
congestion-aware load balancing algorithm in HOLMES, to optimize the storage complexity
while improve the execution rate of the load balancing algorithm.
C. Correlations between the Temporal and Spatial Solutions
Both the temporal congestion control mechanisms and the spatial load balancing mechanisms aim
to optimize the throughput or latency of a DCN. Next, we try to describe the correlations of the
two types of solutions. Hollot et al [85], apply the classical control system techniques to design
controllers and analyze the stability of the same network system under different congestion
control mechanisms. Since the publication of the first seminal paper [92] by Kelly et al, the
framework of Network Utility Maximization (NUM) has been widely applied in network resource
allocation algorithms as well as the congestion control protocols. Inspired by these solutions, we
design a control theoretic model to describe the correlations between the congestion control
mechanisms and the load balancing mechanisms.
As shown in Fig. 10, the closed-loop based control mechanisms are usually host-based
mechanisms, which are generated in an end controller and will be executed later in the in-network
devices. A congestion control mechanism typically operates on a single end-to-end path, and it
concentrates on the performance optimization of one path. The main disturbance during the
policy execution process is the traffic from other multi-rooted paths.

20
The load balancing mechanisms focus on the multi-path scenarios, and schedule the traffic of
multiple paths to improve the overall performance of all the end-to-end paths. Either solution
needs a feedback signal to guide the traffic scheduling in the upcoming control loop. Thus, the
feedback signal will be transmitted to both the congestion controller and the load balancer after
each transmission loop. The load balancing mechanisms are often implemented together with the
congestion control policies. For example, MPTCP enables the parallelized TCP transmissions
among multiple paths using its load balancing policies. It still realizes the traffic congestion
control using the traditional TCP congestion avoidance algorithms. Therefore, it can be
considered as part of the closed-loop control system in Fig. 10.
D. Architecture Improvements
Some other researchers also try to improve the architecture of the scheduling schemes based on
the DC traffic patterns or application features. Freeway [18] dynamically partitions the multiple
DCN paths into low latency and high throughput paths, and schedules the elephant and mouse
flows separately. DevoFlow [52] uses multipath and changes the design of OpenFlow switches to
enable easier flow aggregation, improving DCN latency and throughput. ADN [77] devolves into
the application level, which concentrates on serving the up layer applications. It deploys a novel
architecture that slices the whole DCN into logically isolated sub-networks to serve different
types of applications. The architecture improvements can be implemented together with the
aforementioned load balancing and congestion control mechanisms, to provide a more
comprehensive performance optimization scheme for DCNs [106, 108].
6. CONCLUSION
This paper presents HOLMES, a novel DCN flow scheduling scheme, which tackles mixed (mice
vs. elephants) data center traffic. Using a stochastic performance model, we first prove the
necessity of isolating mice and elephants with a closed form. We then present the HOLMES
architecture that partitions a DCN into high-throughput and low-latency sub-networks. We further
design a stochastic and global congestion-aware load balancing algorithm that schedules the
corresponding DC traffic to each sub-network. Simulation results show that HOLMES network
partition policy can successfully eliminate the interference between the mouse and elephant data
flows. Finally, we prove that HOLMES flow scheduling algorithm is stable and scalable for
large-scale data centers.
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AUTHORS
Mr. Tim Tingqiu Yuan (ytq@huawei.com) is a Vice President of Central Research Institute,
Huawei Technologies. He has been responsible for research and development as well as
technology planning for over 20 years at Huawei. His research interests include, but not
limited to: packet-based networking, information centric networking, software-defined
networking, future Internet, future terminal devices, artificial intelligence and machine
learning.
Mr. Tao Huang (huangtao@huawei.com) is a Senior Expert of Central Research Institute,
Huawei Technologies. Over 20 years, he has been instrumental to many R&D projects and
products at Huawei.
Dr. Cong Xu(xucong@huawei.com) received his Ph.D. degree in Computer Science from
Tsinghua University, Beijing, P.R.China, in 2015. He is now a researcher at Huawei
Technologies. His research interests include data center, cloud computing, big data,
blockchain, etc.
Dr. Jian Li (jian.li1@huawei.com) works on research technology planning at Huawei
Technologies. Before joining Huawei, he was an executive architect with IBM as well as a
research scientist with IBM Research. He earned a Ph.D. in electrical and computer
engineering from Cornell University.

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