SCHEDULING DIFFERENT CUSTOMER ACTIVITIES WITH SENSING DEVICE

International Journal of Advanced Information Technology (IJAIT) Vol. 2, No.2, April 2012
DOI : 10.5121/ijait.2012.2205 59
SCHEDULING DIFFERENT CUSTOMER ACTIVITIES
WITH SENSING DEVICE
A.Prasanth Rao1
, A.Govardhan2
, and Prasad Pinagali3
1
Reasearch Scholar, Dept., of Computer Science and Engineering, JNTU, Hyd
adirajupppy@yahoo.com
2
Professor, Dept., of Computer Science and Engineering, JNTU, Hyd
govardhan_cse@yahoo.co.in
3
Program Manager, SETU Software Systems Pvt..Ltd., IIIT Gouchibowli, Hyd
prasad@setusoftware.com
ABSTRACT
Most periodic tasks are assigned to processors using partition scheduling policy after checking feasibility
conditions. A new approach is proposed for scheduling different activities with one periodic task within the
system. In this paper, control strategies are identified for allocating different types of tasks (activities) to
individual computing elements like Smartphone or microphones. In our simulation model, each periodic
task generates an aperiodic tasks are taken into consideration. Different sets of periodic tasks and
aperiodic tasks are scheduled together. This new approach proves that when all different activities are
scheduled with one periodic tasks leads to better performance.
KEYWORDS
Scheduling, feasibility, multiprocessor, deadline, synchronous, free slots, activities, configuration
parameter.
1. INTRODUCTION
Real-Time systems are specifically designed for situations where the correctness of an operation
depends not only upon its logical correctness, but also upon the time at which it is performed.
Generally real time applications are event driven and the task should complete its execution
within the deadline and so it should be completely determinable. Events can be classified
according to their arrival pattern. In this context, events can be periodic if their arrival time is a
constant or aperiodic when it is not. An asynchronous task is one which has an arbitrary deadline
and should be modeled simply as a synchronous set [13].
There are many partitioned scheduling algorithm[1,2,3,4,5,6,7] which is used to schedule periodic
tasks [8,9]. However using partitioned scheduling algorithm, tasks are allocated to processors and

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each processor is allocated certain fixed number of execution units. The main disadvantage of
partitioned scheduling algorithm is that the processor is not fully utilized. This means that there
are certain execution time units available and these units are fragmented in the processor. To
overcome the disadvantage of partitioned scheduling algorithm, we have to make use of unused
cycles properly. So other types of tasks such aperiodic tasks, different customer activities such
loading a file, payments,etc. are scheduled with periodic task sets which improve the overall
performance of the system. The excess unused computing cycles (free slots) on each computing
device can be computed and these computing cycles are used to schedule different tasks.
There are certain free slots available at different intervals of time and any one of the free slots
may accommodate only a few execution time units. The individual fragments may not be large
enough, so we can combine all these small fragments to execute a much bigger task. The size of
these free slots is configurable with a parameter, which controls the free cycles availability and
allocation of dynamic tasks to individual processor.
The main objective of this chapter to develop strategies to schedule aperiodic tasks with periodic
tasks and the same model can be extended to schedule different customer activities can be
monitored with one periodic task.
Motivation: Modern mobile devices are packed with lots of computing power with latest
processors and highly energy efficient hardware to offer longer battery life. It becomes easy to
harness that cumulative processing power to process bigger and highly computing intensive tasks
using mobile device cloud. By using mobile server cloud computing technologies, this power can
be harnessed in the network. The application like shopping mall traffic monitoring system. The
practical scenario of a customer who goes to a shopping mall with a mobile phone handset. The
communication system is the mall immediately senses the presence of the mobile device and
sends out a request to this customer for permission to add this device to its network. As soon as
the customer accepts this request, his phone gets added to the network and it starts getting used to
monitor and regulate the customer’s business activities like identification and procurement of
times, bill payments etc. Similar systems can also be used to regulate traffic, identify hot spots
and implement effective crowd control mechanisms. All of these items require mobile devices to
collaborate to increase computation power in order to perform real-time analysis of sensed data.
This paper is organized as follows. Section 2 describes Theoretical Concepts Configuration
Parameter presented in Section 3. Section 4 describes Reserving space for newly created tasks
Sections 5 demonstrate Integrated Procedure to Schedule Different Tasks. Finally, the
Performance Results and future scope are given in Section 6.
2. THEORETICAL CONCEPTS
A periodically sampled control system which is modeled on time triggered approach. Time-
Triggered tasks (τ) are characterized by a quadruple (Ø, p, e, d). The periodic task system
involves execution of independent task system Γ = {τ1, τ2, τ3, τ4… τn}, where each task τj ∈ Γ.
2.1. Assumption about Task System
By analyzing above applications mentioned in the motivation, the assumption of system model
can be presented below

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Periodic Task Model
The periodic task generates a sequence of jobs at each integral multiple of period pi. Each job
must execute in at most ei execution units of time and should complete before its relative deadline
di(equals to period of task). The sensing data from different devices are known be periodic and
assumptions are listed below.
a. The tasks which are generated from different sensors are known to be the periodic tasks. The
different instances (jobs) of the periodic tasks are generated at regular interval of time.
b. All periodic tasks are independent and there is no dependence among these tasks.
c. These types of tasks may generate another type of tasks known to be aperioidc or activities.
Before presenting finding free-slots algorithm we need to define Basic Terminology.
2.2. Basic Terminology
In this section we look at definitions which help us to understand the partition parameter and
using this parameter we can dynamically configure processor window.
Definition 2.1: (Total Execution Period Pmax). The total execution time units of a given task
system Γ1
is equal to or less than total execution period (Pmax), then the task system is feasible on
uniprocessor system.
),.................,,.........,,max( 321max nppipppP = ……(1)
Definition 2.2: (Maximum Execution Units emax). emax is maximum execution units which is
defined among a set of n tasks.
)e...,,e,e,max(ee m321max = ……(2)
Definition 2.3: (Configuration Parameter δ).The configuration parameter δ divides the time
axis into two windows. One window is used to schedule periodic task sets and the other window
is used to schedule aperiodic task sets.
Definition 2.4: (Scheduling Condition). The general scheduling condition given RMCT [2]
[ ] max(P)11maxmax
e+ep/P≥P ……(3)
Definition 2.5: (Cut-Off Configuration Value). [δcut-off 1] is known to be feasible region and if
δ< δcut-off then atleast one periodic task cannot be allocated
Using the above definitions we can understand partition condition which divides processor
window into two parts. Before defining partition condition we need to explain about task
execution modeling in next section.
2.3. Task Execution Modelling
A scheduling algorithm provides a set of rules that determine the processor(s) to be used and
tasks to be executed at any particular point of time. There many scheduling algorithm were
presented in the literature [7, 10, 11] and also scheduling heuristics [8, 13] developed. These

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entire algorithms are allocating tasks to the processors using partition scheduling policy which
results some unused free slots on each processor. Also we configure these unused free slots to
schedule different type of tasks together. For further improvement in resource utilization if we
make use of these free slots to schedule dynamic tasks.
2.4. Scheduling Conditions
The schedulable condition for task sets scheduled under RM is based on utilization of a processor
and period oriented. All scheduling conditions which were mentioned above are oriented towards
utilizations i.e. the relative value of task utilization was taken into account. The performance of
these algorithms is limited because they fail to consider the relative values of task periods. There
are many period oriented scheduling algorithms were developed RMGT [8] RMCT [2] and
utilization based algorithms [3][8].
The Rate Monotonic Critical Tasks (RMCT) algorithm is developed based on the maximum
execution period (Pmax) and assumes all tasks in a queue are arranged with decreasing period. The
total execution units (T) of all incoming periodic tasks can be computed and the RMCT may
allocate maximum possible tasks to given processor till condition 4 satisfied. The RMCT
Algorithm [2] identifies the number of processors and also total execution time units (T) given to
each processor. The δ in the if loop known be configuration parameter.
If (T>δPmax) then
{ Increment processor index. ….(4)
else
{Allocates to same processor
}
In the following section we show how this condition in 4 [2] helps to regulate the task
being scheduled.
3. CONFIGURATION PARAMETER
Let us consider task system Γ1
{τ1, τ2, τ3 } and τ1=(5,2), τ2=(7,1), τ3=(10,4). Apply RMCT [2]
algorithm, pmax=10, T=10 units, so all tasks are allocated to only one processor. In this situation
δ=1 , when processor fully loaded with periodic set as shown Figure 1.From figure we conclude
that the processor fully loaded and there will be no free slots available and these type of tasks
should meet deadline.
δ=1
Figure 1. Task allocation to processor 1
However when we change δ=0.8, we require two processor to schedule above tasks system as
shown in Figure 2. From the figure we conclude that two processors required to schedule above
task system and each processor some free slots are available.

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Figure 2. Tasks allocation two processor system
However we can further increase these free slots by decreasing value of δ. The δ=0.4 as shown in
Figure 3.
Figure 3. Task allocation three processor system
In this situation, minimum of three processor required and each processor can allocate one
periodic tasks. However it may increase number of processor but there will be more number of
free slots is available. This helps us to schedule different type of tasks together and we mix up
both high priority and low priority tasks. Not only that an aperiodic tasks whose generation not
known in advance can be scheduled with periodic tasks. The configuration parameter dynamically
can change depending upon the application. So in order to regulate the proportion of aperiodic
tasks we consider a configuration parameter δ and must be selected such that both periodic and
aperiodic tasks can be scheduled together. δ is chosen such that at least one periodic task is

64
allocated to an individual processor. δ, the configuration parameter divides the available window
into parts ,where one part is reserved for fixed priority algorithm [4]and other part is dynamic
priority algorithm[10]. We observe that for further decreases of δ value, there will be at least one
periodic task cannot be allocated any processing element (Theorem 1).
By choosing an appropriate value of δ, we can use our scheduling algorithm in two different
ways. Firstly, it can be used to schedule the task set on an individual processor after checking
feasibility analysis. Secondly, it can be used to find free slots on each processor and in turn these
are used for allocation of dynamically created tasks. This is called as the Partition Condition
which is discussed in the next section.
3.1. Partition Condition
The partition condition divides window into two parts where one window can be used for
scheduling periodic tasks and other window is to schedule aperiodic tasks. The theorem 1 is
proposed which states that the window is divided in such a way that at least one periodic task is
allocated to each processor.
Theorem 1: Given periodic task system Γ1
{τ1, τ2, τ3, τ4… τn } , the partition condition states that
each processor allocates at least one periodic task using configuration parameter δ and its value
lies between [δcut-off, 1]. Where δcut-off=emax/pmax
Proof: Let Γ1
{τ1, τ2, τ3, τ4… τn } be n tasks and all tasks are arranged with increasing priorities
and first in queue will be given least priority.
Let τn, τk be two tasks whose maximum periodicity (Def.3.2) and whose maximum execution
time (Def.3.7) are (pmax) and (emax) respectively.
If ei<pi then taski is schedulable on processor j otherwise the task is not feasible. This implies that
there will be a task whose maximum execution units are emax and all other tasks are in a queue
below this value. For any given task τk ,pk<pmax and that implies emax <pmax. This means minimum
δcut-off equals to emax/pmax and its maximum value equals 1.The configuration parameter value
always lies in between [δcut-off, 1].So the minimum execution units allocated to each processor
equals emax so that δ value is selected in the range [δcut-off, 1]. There will be no task allocated to
processor if δ< δcut-off and so at least one periodic task is allocated to processor if δ lies in the
range [δcut-off, 1]. Hence Proved
Depending upon the type of application, the value of δ can be set, based on this value the
processor allocates fixed number of periodic tasks and also has few free slots to accommodate
aperiodic tasks. Three different portions observed from graph are shown in Figure 4 which is
presented below.

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Figure 4: Feasible Region Graph
The Figure 4 is drawn between configuration parameter and processing elements required for
computing the given load. The observations of three regions from Feasible Region Graph are
listed below.
Region I: Configuration parameter value lies in between [0, δcut-off). So task allocation cannot be
done properly and some tasks are unassigned to processing elements. When δ =0, none of the
tasks can be assigned.
Region II: Configuration parameter value lies in between [δcut-off, 1]. When the value changes
from δcut-off to 1, the number of processing elements required for computing a given task system
decreases. However, maximum number of free slots are available on each processor at δ= δcut-off,
when the value of δ increases further then δcut-off , the number of available free slots decreases.
Region III: If the value of the parameter δ exceeds 1 then tasks are assigned with lesser number
of processing elements. However, they will not meet the deadline and also they will not be RM
schedulable.
Region II is best suitable for scheduling periodic tasks, adjusting parameter δ, different types of
tasks are scheduled together.
The same model can be extended to schedule customer activities or sporadic task system [4].
When new task arrives at processor mi , at phase Ø with deadline di and execution time ei it is
scheduled between the time interval Ø and Ø+di. In order to allocate dynamic tasks, development
of an integrated procedure to schedule different types of tasks is needed. If the available free slots
are not sufficient for allocation of dynamic tasks then it becomes necessary to split them among
multiple processing elements. So the next section3.2 presents conceptual ideas to develop
appropriate scheduling algorithms.
3.2 Conceptual Foundations
Before presenting new algorithm RMCT-Split, one is required to understand certain concepts to
design and implement an algorithm to schedule the task sets.
Task Splitting
As mentioned earlier, partitioned scheduling algorithm RMCT allocates fixed number of tasks to
an individual processor and by doing this there will be some unused free time slots on each
processor. This unused free space may be a very small fragment and all the available small

66
fragments can be combined to form a much bigger space. In order to execute a bigger task, it
should be split across multiple processors. This idea has been used by several researches [2, 3, 4,
7] for scheduling sporadic tasks or periodic task with implicit deadline. In this work, the task
splitting is applied to aperiodic tasks or constraint deadline or arbitrary deadline. Our work
mainly focuses on the possibility of splitting newly arrived task into two or more pieces and
allocating them on different processing elements. Our approach is similar to previous works but
differs in the following aspects
Task assignment and splitting of task mechanism is based on total execution units in a
particular interval of time.
The period oriented condition can be used instead of utilization based schedulable test.
Different types of tasks are tried for scheduling on the same processor; if that is not possible,
task splitting among multiple processing elements is performed.
The Dispatching algorithm in the task model addresses two important issues
Ensures that two pieces of the same task do not execute simultaneously on different
processors.
Schedulable test is performed between two intervals.
Fixed numbers of processors are grouped together and task splitting scheme is used among those
processing elements only. This helps us to improve system throughput, response time and in
reduction in latency time.
Dispatching
Different processors harmonize in time when task can be split into two pieces to execute on these
processing elements. One piece of split-task is allocated to processor m1 where reserve space is X
[m1] and other piece is allocated to processor m2 where reserve space is Z [m2].The non-split task,
assigned to processor m with earliest deadline is selected for execution.
When a new task arrives at processor mi, at phase Ø with deadline di and execution time ei it is
scheduled between the time interval Ø and Ø+di. If sufficient time is available in that particular
interval then the task is allocated to the same processor otherwise the task will be split into two
fragments. One fragment is executed at one processor mi and other fragment is executed at
another processor mj. The splitting of the task is done in such a way that the dispatchers on each
processor make sure that the fragment tasks are never executed on two processors at the same
time but one particular split task is always ahead of the other split task.
In this work, task-splitting to aperiodic task with certain time constraints is applied, thus allowing
an individual task to be split between the processors. The same model can be extended to
schedule sporadic task system [4].
Whenever a new task arrives, the algorithm immediately searches for a free slot to schedule the
task locally otherwise it is sent to the group scheduler. A few of the processors are grouped
together known as group scheduler. The splitting of task can be performed within the group and
it searches suitable processor for the newly arrived aperiodic or asynchronous task. An integrated
procedure is desirable to schedule different types of periodic tasks, aperiodic/ asynchronous tasks.
Before presenting an integrated approach there is a need to find free-slot in the given interval, the
necessity of finding free-slots in the given interval will be discussed in the next section 4.2.3.

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3.3. Availability of Slots at Fixed Interval
Initially, the centralized scheduler allocates a fixed number of execution time units to an
individual processor and in each processor available free slots are computed. The total number of
processing elements m will be divided into a number of small groups. Each group maintains a
group scheduler which contains information about all processing elements within it. The total
availability processing capacity within the group equals to sum of the free slots and can be used to
execute a much bigger task. The Algorithm 1 is used to compute free slots and this information is
available at group scheduler. A group scheduler maintains a table which contains information
about each processor-ID, total-execution units, planning cycle (M) and size of fixed free slots. All
the pieces in a split-task should be scheduled within a particular group only.
Let the number of tasks allocated by RMCI algorithm j = nj.
Planning cycle of periodic tasks allocated to processor j=Mj
The number of occurrences l = Mj/phase
Initialize first task in priority queue and fixed slots in the interval given by
1,......0).,,( =∀+ kephaseKphasek jii ……… (5)
Using above formula, fixed slots can be generated apart from available slots. The rest of tasks
which are present in the queue check availability of free slots and each task from queue are
allocated using Algorithm 1. Fixed allocated slots means that tasks which are assigned to
particular processor execute only on mentioned slots. This condition which is used in RMCT is
said to be necessary and sufficient i.e. property of RM algorithm is satisfied. The allocation of
fixed time slots means that the execution of the task is predefined in allocated time frame. This
results in a very low number of preemptions.
Algorithm 1. Finding Free Slots
I. for(j=0;j≤m;j++)
a) Read number of tasks (nij ,M,Phase);
for i=0;
//First task only.
Occurrences l = M/phase
b) for (k=0;k≤l; l++)
Slots fixed for taski= [k*phasei, K*phasei + eij]
Available slots =[ K*phasei + eij, (K+1)phase)
II. for (i=1;i≤nij ;i++)
{
Check in available slots.
Occurrences l=M/phasei
i. for (k=0; k<=l;k++)
{
Pick up one by one available slot
If (upperbound-lowerbound>=eij)
Slots fixed = [lower bound,
lowerbound+eij]
Available slot =[lowerbound+eij, upper
bound]
else
Keep available slot as it is.
}
}

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The group scheduler maintains a status table which contains information about availability of free
slots at the given planning cycle. The main objective of group scheduler is to allocate available
free slots to processing elements which request for them and sharing of processing capacity
within the group only. This helps us to decrease communication delay among processing
elements. The next section proposes how to make use of these unused processing capacities for
newly created dynamic tasks.
4. RESERVING SPACE FOR NEWLY CREATED TASKS
On processor p, identify free slots available in the interval Ø and Ø+ di. If any one of the free
slots is sufficient to accommodate newly arrived task then that task is allocated to that particular
processor otherwise task is split into two fragments such that one fragment is allocated to one of
the available processors and other is allocated to another processor. The splitting can be
performed in such a way that the task executes in given group only, otherwise this task is rejected.
Let the space reserved on processor mi for one portion of the split-task be x[mi] and the space
reserved for second portion of the split-task on processing element (mj) be z[mj].Likewise all the
parts of the split-task reserve spaces on processors which are within the group. The dispatching is
simple. If processor mi reserves at time t and other portion of the split task is assigned to another
processor mj it reserves after time t + x [mi].
Assume S1, S2,…,Sn are the sizes of free slots available on the processor in the interval
(0, M].The free slot which has the maximum size, has to be identified and has to be denoted by
Smax.
Smax = maximum slot size within the interval Ø and Ø+ di.
Smax = max (S1, S2,..Sk), where k free slots are available in the mentioned interval.
The space reserved for one portion of task should be equal to Smax i.e. x [mi] = Smax
Next suitable processor mj should be searched for the remaining portion of split-task such that
Z[mj] = eij - Smax
Where eij is the execution time of task i on processor j.
Likewise a bigger task can be split into smaller fragments and allocated to the processing
elements.
When a dynamic task arrives at time t, the task tries to schedule locally otherwise it searches for
free slots in that particular processor group. The algorithm 2 is used for getting number of free
slots in each processor and to find the size of each free slot. The size_free_slots [req_size] and
no_free_slots [req_size] give us the size of free slot and number of free slots in that particular
interval for each and every processing element.
The Algorithm 2 is used for finding optimal free slots and their sizes for newly arrived tasks and
the algorithm tries optimizing among two processing elements. This means the sum of execution
units between two processors is just equal to the computation time of the task. The Algorithm 3 is
used for finding free slots of maximum size within available free slots in each processing
element. The Algorithm 2 and Algorithm 3 can be invoked when a new task arrives and the
status of the availability of slots in the given interval should be known. If the slots are not
available within the group, task is simply rejected and a log file is created for those rejected tasks.
This helps us to increase or decrease the size of the group and will also be useful for proper
assessment of task allocation.

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Once a group scheduler identifies processor for required time units of a given task, it immediately
locks the identified slots.
Finding optimal free-slot in the interval t and t+d for newly arrived task
Algorithm 2. Finding optimal free-slot
//optimal allocation:
optimal_fs_size=size_free_slots
for (int i=0;i<req_size; i++)
{
//pick one value greater than min_req and less than remaining
all
If(size_freeslots[i]≥min_req&& locked[i]=0)
{
If (optimal_fs_size≥size-freeslots[i])
optima_fs_size = size_freeslots[i];
}
}
If (optimal_fs_size<min_req)
{
//assign nearest fsize to splitting task
//find out maximum value so that will get the nearest value
Optimal_fssize=Max(availability_fslot[]);
//lock that processing element;
Locked[j]=1;
min_req=min-req-optimal_fssize;
//repeat optimal allocation block for remaining
}
else
{
//no need to split task directly lock that processing element;
Locked[i]=1;
Lock-index[j] with request processor[i]
}
Finding maximum size of free-slot t and t+d
Algorithm 3. Finding maximum size of free-slot t and t+d
Max(availability_fslot[])
{
Maximum value=0;
for (j=0;j<req_size;j++)
{
If(locked[j]!=1)
{
If (Maximum value<availability_fslot[j])
Maximum value= availability_fslot[j];
}
}
return j, maximum value;
}

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The workload of given application is distributed among m processor system and each processor
maintains local scheduler. The splitting of task can be possible within a certain set of processing
elements and each set maintains group scheduler. The next section presents an integrated
procedure to schedule different types of tasks.
5. Integrated Procedure to Schedule Different Tasks
The integrated approach integrates all three schedulers (local, global and group) to provide a
complete solution to schedule real tasks among different processing elements. This scheme has all
the three components and also takes interactions among different processing elements. Each
processor has a local scheduler and is allocated a fixed number of execution time units in a given
planning cycle. As it is known that, there will be certain free slots available and these intervals are
fixed.
Each group maintains Maekawa’s sets [10] which are chosen in such a way that there will be a
common communicating processing element among different sets that gives equal responsibility
to every processing element in state information exchange, using a minimal number of messages.
Each group of processing elements maintains the following three sets for efficient communication
to other processing elements.
Request Set (Ri): Set of processing element to which the group sends request for state
information.
Inform Set (Ii): Set of processing elements to which it sends information about its state.
Status Set (Si): Set of processing elements in which free slots are available.
The group scheduler maintains a status table which contains Processor ID, fixed total time
execution units already committed to run and number of free-slots in a given planning cycle. The
fixed total execution units are statically allocated using partitioned algorithm known as RMCT
and these tasks are known as critical tasks. The centralized scheduler distinguishes processing
elements into groups of request sets considering certain parameters such as availability of free
slots and communicating processing elements. For a given group of processing elements, the size
of the set can be figured out which can be called set size. But number of processing elements in
each group can be fixed and required number of groups can be computed. Each group can be
given a unique id and there is no communication among the groups but processing elements share
unused space within the group only. Set-size can be given by the square root of number of
processing elements in a group. Where gn indicates that number of elements in a group.
[ ]
[ ]
[ ]sizesetR
Rm
RR
ii
iii
jiji
_.3
.2
.1
=∀
∈∀
≠∀∀ φI
………(6)
Processing element mi is contained in exact set size request sets
There fore
set_size = √gn
1. There is no common element between two groups such as i,j

71
φ=∩ ji GG
φ=∩==∀∀ jiji GGNji ::,1:
The number of groups can be computed which depends on the number of processing elements and
size of each group can be fixed. The total number of groups in a system is equal to ratio between
processing elements (m) and size of the group (gn). REQUEST (i) is sent to all processing
elements in each group to know the availability of free slots in that particular interval of time. All
processing elements send RESPONSE (j) about availability of free-slots and its size.
Example 4.2: The processing elements m=100 divides into 15 groups and each group contains 7
processing elements. set_size=√7 ≈3. There three request set Ri (1, 2, 3), (3, 4, 5) (5.6, 7) are
formed within the group. Each set has a processing element which communicates with the other
sets in the group scheduler about the status of availability of free slots.
In order to use our algorithm, it is necessary to ensure that each task is processed on one
processor only at any point of time. Task splitting must therefore address three important
challenges.
1. Dispatching algorithm to be developed for ensuring that smaller pieces of a task do not
execute simultaneously
2. Design a schedulable test for the dispatching algorithm.
3. Order of execution of all generated pieces is maintained properly.
The next section presents Schedulable Analysis.
5.1 Schedulable Analysis
The processor demand represents the amount of execution that must necessarily be given to a task
in order to meet its deadline. The execution demand of newly arrived tasks at phase Øi,
periodicity (pi) and deadline di should always in between Øi and Øi+di. The processor demand of
taski is in the planning cycle (0, M] and all tasks which are released in this planning cycle should
obey following conditions.
a) Should arrive not earlier than beginning of interval
b) Should have deadline no later than the finishing of time interval.
The processor demand of a task set is defined analogously. Let dbf (Ttotal , M) denote the
processor demand of task set τ of time interval (0, M] where M is planning cycle. Ttotal is equal to
sum of execution units of k tasks on given processor j.
Ttotal = Tj + Tedf ….… (7)
Tj= Fixed execution units allocated using theorem -1
Tedf = Addional execution units added to processor i.
The Tedf can be computed dynamically using earliest deadline first algorithm. When an aperiodic
task arrives at phase Ø, execution time ei and deadline di on processor mi then invoke algorithm
for finding free slots in given interval. Sopt be optimal execution units in a given processor group.

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The space reserved for one portion of task should be equal to Smax
So, x [mj] = Sopt
If the Sopt is equal to execution units ei of task i then that task is allocated to the processor j
otherwise suitable processor is searched in the same processor group. The remaining portion of
split task can be computed as Z[mj+1].
i.e. Z[mj+1] = ei - Sopt
The Tedf for processor j and j+1 can be updated with x [mi] and Z[mj+1] respectively in the
interval Ø and Ø +d.
Tj fixed units are allocated to individual processor using partitioned algorithm known as RMCT
and Tedf is computed using free slots algorithms. The allocation of all newly arrived tasks in τ are
met if and only if
MMdbfM ≤>∀ ),(,0 τ ……… (8)
The above schedulable condition gives us processor demand of a taski in the of interval between
task release time and its completion time. This means that total execution units are less than or
equal to M. The above condition fails when there is no enough free space on the processor to
accommodate a newly arrived task. So in this scenario the task should be split according to
algorithm mentioned above.
6. PERFORMANCE RESULTS
By making some minor changes to the set up used by Anderson [4], the periodicity (p) values
ranging from 1 to 1000 are uniformly distributed. Experiments are performed for two processor
and eight processor systems. In our simulation model, execution times may be drawn only from
bimodal. According to Bimodal tasks can be heavy and light which can be given any random
utilization value from the intervals [0.5, 1) and (0.0, 0.5) respectively. The execution times of task
τi are chosen such that it is equal to pi times randomly chosen utilization value in given interval.
Experiments were performed for periodic task sets and deadline of each task should be equal to
its periodicity.
Initially using partitioned scheduling algorithm, fixed number of execution units are allocated to
the individual processor with fixed value of configuration parameter (k). The task set generator
which is developed is used to check feasibility of individual task set and individual task. The task
sets with 1
1
1
≥∑=
n
i i
i
p
e
m
are immediately rejected by the task set generator and also at least one
task in task set which has ii pe > is rejected as well.
We run multiple experiments and in each experiment task set generator developed by us is used
which generates more than 1000 task sets. These task sets are written in a file and this file is fed
as input to our algorithms. For simulation J.Anderson and RMCT_Split algorithm are
implemented and the same input is given to these two algorithms.

73
For each task set, the utilization is calculated and it is put it into the bucket. There are 100 buckets
and each bucket is used for each percentage of utilization. For example all task sets with
utilization within [0.5 0.4) are put the one bucket. For each bucket the number of task sets can be
calculated which are scheduled with each algorithm considered. All tasks in a given task set meet
feasibility conditions otherwise particular task set is rejected by our generator. Our simulation
results can however be used to find number of task sets feasible for m=2 and m=8 as well. This
gives us a few tasks which can be split and allocated to two processor or eight processor systems.
The results from bimodal distribution are shown in Figure 5 to 6.
The y-axis should have been labelled “number of task sets “and x-axis “total utilization of each
task set”. The graph tells us the number of task sets that were schedulable for each utilization
range. In turn, each task set might consists of 10, 18, 25…etc. tasks or even small number of tasks
but we are interested about total utilization of each task set. From these experiments we conclude
that more number of free slots is available in RMCT algorithm and these free slots are utilized for
newly created aperiodic tasks. By adjusting parameter k more number of aperiodic task sets is
allocated to a processor. However, processor utilization never exceeds one but we should have
proper mix of aperiodic tasks and periodic tasks.
Figure 5. Bio Model m=2
Figure 6. Bio Model m=8
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9
0
1
2
3
4
5
6
7
x 10
4 biomodel m=2
ANDERSON
RMCT-SPLIT
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9
0
1
2
3
4
5
6
7
x 10
4 biomodel m=8
ANDERSON
RMCT-SPLIT

74
6. CONCLUSIONS
This paper provides solution to make use of unused free-slots and to schedule different types of
tasks with periodic task sets. Initially, the newly created dynamic tasks were tried to schedule to
one of the processors available but in a few cases CPU cycles were not sufficient to execute a
given task. In such scenarios splitting can take place between two processors which improves
better resource utilization. Only a few processors are grouped together using Mekava set which
reduces communication delay. Simulations were conducted for 100 to 200 tasks. This work which
includes RMCT algorithm to schedule different types of tasks shows better results than that of the
previous work. Whatever algorithms which were developed are purely deterministic and task
nature was predictable in that particular type of environment.
This paper predominantly considers a control strategy for allocating different types of tasks or
activities are scheduled with periodic tasks. Also strategy for allocating at least on periodic task to
an individual processing element and remaining unused cpu cycles are used for allocating
different activities. The same principle can be extended to schedule different activities in
shopping mall and traffic monitoring system. In shopping mall and traffic monitoring system
communication among customer through mobile devices. In this scenario all customer activities
are monitored through mobile devices and each device possesses at least one sensor and rests of
CPU cycles are used for other activities. Our feature work performs real-time analysis of sensed
data to collaborate to increase computation power and development such type of device.
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[1] C.Liu and J.LayLand, “Scheduling Algorithms for Multiprogramming in Hard Real–Time
Environment,” JACM 10(1), 1973, pp, 174-189
[2] A.Prashanth Rao and A. Govardhan, “An Improved Period Oriented Scheduling Algorithm for Real
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[3] S.Cheng, J.A.Stankovic, and K.Ramamritham, Scheduling Algorithm for Hard Real Time Systems: A
Brief Survey, Tutorial: Hard Real Time Systems, EFF Press, 1988, pp 150-173.
[4] J. D Gafford, Rate Monotonic Scheduling, IEE Micro, June 1991, pp 34-39 Real Time Systems by
James W.S.Liu Published by Pearson Education, II Ededition, 1991.
[5] D.S Johnson, Near Optimal Bin Packing Algorithms, PhD Thesis, MIT 1973.
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[7] Edited by Mathai Joseph, Real-time Systems Specification, Verification and Analysis, Tata Research
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[10] C.Siva Ram Murthy and G.Manimaran, Resource Management in Real-Time Systems and Networks,
PHI Learning Private Limited, 2009.
[11] D. Zmaranda, G. Gabor, D.E. Popescu, C. Vancea, F. Vancea, Using Fixed Priority Pre-emptive
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[12] Rodolfo Pellizzoni,Giuseppe Lipari,Feasibility Analysis of Real-Time Periodic Tasks with Offsets,
Real-Time Systems,Kluwer Academic Publishers Norwell, Volume 30 Issue 1-2, May 2005
[13] Bjorn Anderson, Konstantin’s Bletsis, Sanjoy Baruah, Arbitrary-Deadline Scheduling Sporadic Tasks
on Multiprocessor, Technical Report HURRAY-TR-080501.

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