finite-source queuing model (sometimes called the finite-population, machine-interference, or machine-repairman model), which has often been used in analyzing time-sharing systems and multi- programmed computer systems, is invesugated. The model studied here has two service staUons, a processor (single server) and peripherals (infinite server), and a finite number of customers (or jobs) that have a distract service rate at the processor. The model is in eqmhbnum. It is shown that the utilization factor of the processor can be obtained in an analyuc form and ts independent of various scheduling disciphnes employed at the processor, such as FCFS, generahzed processor sharing, preempUve (resume) and nonpreemptwe priority disciphnes, under some condiaon. Other relevant propemes of this model are also shown. The range within which these properties hold is discussed, and some examples are given. Examples of appficatlon to multiprogrammmg and tune-sharing systems are given; in particular, It Is shown that the often used dynamic dispatching pohcy (which gwes the higher preempuve priority to the more I/O oriented job) is optimal within the framework of this multiprogramming model. Categories and SubJect Descriptors:

A Finite-Source Queue with Different Customers

It has been claimed on the basis of empirical studies that a CPU scheduling policy, whereby I/Obound jobs are given preemptive priority over CPU-bound jobs, produces the highest overall CPU utilization of multiprogrammed computer systems. However, a theoretical result has shown that the CPU utilization is independent of CPU scheduling in a finite-source queuing model of multiprogrammed systems. This paper aims at resolving this seeming conflict and gaining some insight into CPU scheduling by analyzing a Markovian model of job-stream processing. The model studied consists of an infinite backlog of jobs of two classes (a job stream} and a multiple-resource system (the model of a multiprogrammed system which processes the job stream}; the system consists of a cyclic queue of two nodes--a single (CPU) server and an infinite (I/O) server. The system contains a fixed number of jobs concurrently; the values of parameters describing each job class are distinct except for the mean I/O service time. The following result is obtained under the near-complete decomposability of the model: The maximum overall CPU server utilization (and the maximum throughput) is achieved by scheduling policy whereby jobs of the class having a shorter mean CPU service time are given preemptive priority over others at the CPU server, although the CPU server utilization is independent of CPU scheduling so long as the set of jobs in the system remains fixed.

http://www.osdp.cs.tsukuba.ac.jp/kameda/MyPapers/MyACMPapers/p78-kameda.pdf

Optimality of scheduling policy for processing a job stream

Model studies of some integrated, feedback-driven scheduling systems for multiprogrammed-multiprocessor computer systems are presented The basic control variables used are the data-flow rates for the processes executing on the CPU The model systems feature simulated continuous-flow and preempt-resume scheduling of input-output activity Attention is given to the amount of memory resource required for effective processing of the I/O activity (buffer space assignment) The model studies used both distribution-driven and trace-driven techniques Even relatively simple dynamic schedulers are shown to improve system performance (as measured by user CPU time) over that given by optimal or near-optimal static schedulers imbedded in identical system structures and workload environments The improvement is greatest under a heavy I/O demand workload

Feedback coupled resource allocation policies in the multiprogramming-multiprocessor computer system

A computer program to predict the performance of local area networks based on an Ethernet or other medium is described. The effects of bursty traffic are modeled as packet streams which are initially bulk Poisson, but whose clusters spread apart as they propagate through the network. It is shown by example that performance predictions using more conventional Poisson assumptions tend to be optimistic, often extremely so. The program presents a friendly, dialogue-oriented user interface, including a library of rather sophisticated transaction types for network loading. A simulator is included in the program to validate its analytical approximations, and two example simulations are presented. Although approximation errors can be large in highly bursty situations, these errors appear to be much less than those which would be obtained by treating bursty traffic as if it were Poisson.

Bursty Traffic Local Network Modeling

(Abstract) Policy based network management is a promising approach for provisioning and management of quality of service in mobile ad hoc networks. In this thesis, we focus on performance evaluation of this approach in context of the amount of service received by certain nodes called policy execution points (PEPs) or policy clients from certain specialized nodes called the policy decision points (PDPs) or policy servers. We develop analytical models for the study of the system behavior under two scenarios; a simple Markovian scenario where we assume that the random variables associated with system processes follow an exponential distribution and a more complex non-Markovian scenario where we model the system processes according to general distribution functions as observed through simulation. We illustrate that the simplified Markovian model provides a reasonable indication of the trend of the service availability seen by policy clients and highlight the need for an exact analysis of the system without relying on Poisson assumptions for system processes. In the case of the more exact non-Markovian analysis, we show that our model gives a close approximation to the values obtained via empirical methods. Stochastic Petri Nets are used as performance evaluation tools in development and analysis of these system models. Acknowledgements I would like to take this opportunity to express my deep appreciation and thanks to all those who helped me through the process of conducting this research. First and foremost, I am truly grateful to Dr. Luiz A. DaSilva for his constant support and encouragement throughout this research journey. He was an incessant motivating force in realizing this thesis. He was extremely patient and always provided me with an " active ear " to all the queries and problems I encountered during the course of this research. His relentless efforts to improve my technical writing skills are commendable. I would also like to thank Dr. Kaustubh Phanse for his instrumental role in driving me to conduct research in this area. He truly laid the foundation for this research by his own doctoral work and always provided a guiding hand through all the time he was at Virginia Tech. Away from Virginia Tech, he has been doing all he can in his ability as a mentor and a committee member to help me through various technical and non-technical difficulties I faced. One person who has always awed me as a teacher and a researcher is Dr. Midkiff. He …

Stochastic Petri Net Models of Service Availability in a PBNM System for Mobile Ad Hoc Networks

Scheduling in the central server queueing model, consisting of a "CPU" server and m "I/O" servers, is considered for the case of two customers. Optimal (maximal CPU utilization) CPU and I/O schedules are obtained. The best CPU schedule depends on the I/O schedule in effect; and is either Longest or Shortest-Expected-Remaining-Processing-Time-First. However, for certain I/O schedules the CPU schedule is immaterial. The best I/O schedule is always to process the longer CPU customer first.

Multi-queue scheduling of two tasks

A class of schedules in the two customer central server queueing model, consisting of a “CPU” server and m “I/O” servers, is considered. Optimal (maximal CPU utilization) CPU and I/O schedules are obtained. The best CPU schedule depends on the I/O schedule in effect; and is either Longest or Shortest-Expected-Remaining-Processing-Time-First. However, for certain I/O schedules the CPU schedule is immaterial. The best I/O schedule is always to process the (expected) longer CPU customer first.

In this paper, we propose a class of queueing network models, and a method for their approximate solution, for computer networks with bursty traffic and finite buffer space. The model is open, implying no population limit except for buffer size limits and therefore no window-type flow control mechanism. Each node of the computer network is represented as a finite-length queue with exponential service and an arrival process which is initially bulk Poisson, but becomes less and less clustered from hop to hop. Elaborations are possible to account for varying mean packet sizes and certain buffer pooling schemes, although these involve further approximation. The approximations of the method were validated against several simulations, with reasonable agreement, and certainly with much less error than is obtained by modeling a bursty traffic source as Poisson.

Jeffrey R. Spirn

Papers

Multi-queue scheduling of two tasks

Multi-queue scheduling of two tasks

Network modeling with bursty traffic and finite buffer space