Feedback Queueing Models for Time Shared Systems
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The document discusses scheduling methods for threads and processes in computing, emphasizing the importance of balancing system resources and providing quality service. It explains various models, including round-robin and priority-based scheduling, and their impact on average waiting times in queues. Key concepts such as stochastic processes and the Markov property are introduced, highlighting their relevance to predicting future states in scheduling scenarios.
Feedback Queueing Models for Time Shared Systems
- 1. Present By : Ishara Amarasekera Prabath Weerasinghe By Edward G. Coffman and Leonard Kleinrock
- 2. • Stochastic Process – A process that describes the data of a random process. • Markov Property - The memory less characteristic of stochastic process. • Memory less - Future state can be predicted without knowing the previous states 1
- 3. What is Scheduling? Scheduling is the method by which threads, processes or data flows are given access to system resources. Why need Scheduling? To load balance and share system resources effectively or achieve a target quality service. 2
- 4. P QUEUEA(t) PROCESS OR B(r) q • Units arrive from infinite source • Units take the end of the queue immediately on their arrival • Served a fixed amount of service (q) on FCFS basis • If a unit being served completely within q, it exits the system • If not, is removed from the processor and put back to the end of the queue How it works 3
- 5. • Once all units ahead are served, the interrupted unit is again served. –Preemptive Resume • The same will continue for all the units in the queue How it works P QUEUEA(t) PROCESS OR B(r) q 4
- 6. • Average service time B(r) and Average arrival time A(r) is constant • Q = Total Capacity or No. of instructions can be processed per second • n= No of units per second • Therefore, Q/n = Amount of capacity shared among each unit per second. . Consider RR system in which q 0 Q PROCESSOR q 0n 5
- 7. • Thus the processor is being shared among all units with Q/n amount. This leads to a Processor Shared Model By making all units in the system receive service concurrently and experience no waiting time in the queue. Consider RR system in which q 0 Q PROCESSOR q 0n 6
- 8. • Input traffic is broken into P separate priority groups. • Service Time given to a unit with priority p when q = 0 = gpq • when q = 0 Service Time given to a unit with priority p = gp/ ∑ gini f1 f1 . . f1 f2 f2 . . f2 . . fp fp . fp . . ƛp N1 PRIORITY UNITS N2 PRIORITY UNITS NP PRIORITY UNITS • Unit with priority p might get a service time which is > Q/n due to it’s priority • A generalization of the processor shared model. gp = Priority group ni = number of members from the group I present in the system 7
- 9. How it works PROCESSOR q ƛ N 2 1 : : P • Unit at the service point at any given queue level will not be serviced unless all tower level queues are empty •Unit at service is given a quantum (q) of service like in the RR model •If q is not enough, the unit will be subsequently placed at the end of the next higher level queue 8
- 10. When q 0 and N is finite it gives a FCFS Model When q 0 and N is infinite it gives a RR Model i + 1 i : PROCESSOR q ƛ N 1 P : 9
- 11. i + 1 i : PROCESSOR q ƛ1 1 P : ƛ2 ƛp • Different quantum sizes for different levels and different mean times for different priory-level units are given. • Units can come from outside. •Until the Lowest level is the highest priority queue is processed they need to wait. 10
- 12. • For all the models no overhead or swap time is associated with the process of unloading and loading units from the processor . • Therefore the results may be viewed as upper bound of system performance. 11
- 13. • Process with smallest time will be processed first • Waiting time in the queue W(t). • Non pre emptive, therefore this results slow response time to new jobs. t - service time λ - Arrival rate µ - Service rate 12
- 14. RR – Round Robin Processor-Shared Models(q -> 0) Priority Processor-Shared Model Multiple Level FB Model Priority Based Multiple Level FB Model Shortest Job First FCFS When q limits to zero q -> 0 With priorities assigned – gp With priorities assigned – gp 13
- 15. • Performances differ on each model. • So need to analysis before recommending. • Using Average Waiting Time W(t) is a good choice. Wait.. define Average Waiting Time. 14
- 16. “Average wait time for a given model is the sum of the time spent in queues and the service.” 15
- 17. • Considering q ≠ 0 and time in service as negligible, only the time in queue is taken to calculate the average wait time. • In FBN N -> α • Wk = W(t) – t • A graph is drawn with the average waiting time Wk against the load ƿ. • Load ƿ can be considered as the number if arrivals per service. ƿ = λ/μ 16
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- 19. •FCFS is used as a reference. •With respect to that; o The average waiting time behavior of FN and RR models at low load values. o Which one is better for short service time units ? o Which one is better for longer service time units ? 18
- 20. • When q ≠ 0, N -> α, λ = 0.5 sec, μ = 1.0 sec • Two separate graphs for both RR and FBα with two events. • 2 seconds service time event and 0.5 sec service time event. 19
- 21. What is this ? Why is this saw tooth shape ? What explains the upper envelope slope….. 20
- 22. Same questions can be asked as of the RR model 21
- 23. • Why those serrations ? • What makes the increasing slopes ? • What makes the decreasing slopes ? • Reasoning the behavior between two discontinuities ? 22
- 24. Unit with 2 sec service time. System with 1 sec average service time. Model A : q = 2.0 – ε Model B : q = 1.0 – ε What would contribute to the wait time the most ? 23
- 25. •Number of levels = 4 •Below 2/3 sec quantum size -> Sends the unit to level 4 24
- 26. •Processor-Shared Model •Preemptive Processor-Shared Model •Shortest Job First All the above get analyzed in two graphs. 25
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- 29. • Round Robin Model : Late – Arrival Systems Average Wait Time 28
- 30. • There’s one in all kind of scheduling model. • All are different in their own ways and usage differs with the applications • According to the Conservation Law : - Any favors to some units would result in a discrimination of some others. • This is because of having a constant CPU capability. 29