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"Mitrani, I"
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Analysis and synthesis of computer systems
Analysis and Synthesis of Computer Systems presents a broad overview of methods that are used to evaluate the performance of computer systems and networks, manufacturing systems, and interconnected services systems. Aside from a highly readable style that rigorously addresses all subjects, this second edition includes new chapters on numerical methods for queueing models and on G-networks, the latter being a new area of queuing theory that one of the authors has pioneered.This book will have a broad appeal to students, practitioners and researchers in several different areas, including practicing computer engineers as well as computer science and engineering students.
eBook
Towards power-elastic systems through concurrency management
This study describes power-elastic systems, a method for designing systems whose operations are limited by applicable power. Departing from the traditional low-power design approach which minimises the power consumption for given amounts of computation throughput, power-elastic design focuses on the maximally effective use of applicable power. Centred on a run-time feedback control architecture, power-elastic systems manage their computation loads according to applicable power constraints, effectively viewing quantities of power as resources to be distributed among units of computation. Concurrency management is demonstrated as an effective means of implementing such run-time control, through both theoretical and numerical investigations. Several concurrency management techniques are studied, and the effectiveness of arbitration for dynamic concurrency management with minimal prior system knowledge is demonstrated. A new type of arbitration, called soft arbitration, particularly suitable for managing the access of flexible resources such as power, is developed and proved.
Journal Article
Large Scale and Heavy Traffic Asymptotics for Systems with Unreliable Servers
The asymptotic behaviour of the M/M/n queue, with servers subject to independent breakdowns and repairs, is examined in the limit where the number of servers tends to infinity and the repair rate tends to 0, such that their product remains finite. It is shown that the limiting two-dimensional Markov process corresponds to a queue where the number of servers has the same stationary distribution as the number of jobs in an M/M/[infinity] queue. Hence, the limiting model is referred to as the M/M/[M/M/[infinity]] queue. Its numerical solution is discussed. [PUBLICATION ABSTRACT] Next, the behaviour of the M/M/[M/M/[infinity]] queue is analysed in heavy traffic when the traffic intensity approaches 1. The convergence of the (suitably normalized) process of the number of jobs to a diffusion is proved.
Journal Article
THRESHOLD POLICIES FOR A SINGLE-SERVER QUEUING NETWORK
We consider a single-server queuing system with two
job classes under service policies of threshold type.
The server switches from type 1 to type 2 when either the
former queue is empty or the latter reaches size T;
it switches from type 2 to type 1 when the former queue size
drops below T and the latter is not empty. The joint
queue-length distribution is determined for preemptive and
nonpreemptive implementations using both analytic techniques
and the power series algorithm.
Journal Article
A semidefinite programming approach to the optimal control of a single server queueing system with imposed second moment constraints
Classical analyses of the dynamic control of multi-class queueing systems frequently yield simple priority policies as optimal. However, such policies can often result in excessive queue lengths for the low priority jobs/customers. We propose a stochastic optimisation problem in the context of a two class M/M/1 system which seeks to mitigate this through the imposition of constraints on the second moments of queue lengths. We analyse the performance of two families of parametrised heuristic policies for this problem. To evaluate these policies we develop lower bounds on the optimum cost through the achievable region approach. A numerical study points to the strength of performance of threshold policies and to directions for future research.
Journal Article
Response Time Problems in Communication Networks
Two problem areas are discussed. The first concerns the distribution of sojourn, or response times in networks which allow overtaking. Exact results for a few special cases are presented. The second problem area has to do with determining the average response times in local area networks under particular communication protocols. Models which do not lend themselves to exact solution are studied approximately.
Journal Article
A Characterization of Waiting Time Performance Realizable by Single-Server Queues
In this paper we study the problem of designing scheduling strategies when the demand on the system is known and waiting time requirements are pre-specified. This important synthesis problem has received little attention in the literature, and contrasts with the common analytical approach to the study of service systems. This latter approach contributes only indirectly to the problem of finding satisfactory scheduling rules when the desired (or required) response-time performance is known in advance. Briefly, the model studied assumes a Markov queueing system with M (priority) classes of jobs. For each class, a desired mean waiting time is given in advance. Making use of a well known conservation law, we prove a necessary and sufficient condition for the existence of a scheduling strategy that achieves the desired performance. We also give a constructive procedure for checking the condition and, if a solution exists, a procedure for finding one such strategy. Our assumptions are discussed and the possibility of relaxing them is explored.
Journal Article
Note--A Critical Note on a Result by Lemoine
In a recent paper [Lemoine, A. J. 1977. Networks of queues—a survey of equilibrium analysis. Management Sci. 24 (4) 464–481.], A. J. Lemoine has derived an expression for the Laplace transform of the residence time T of a customer in a feed-forward exponential network. That expression was used to obtain the first two moments of T and the results agreed with those obtained earlier by Reich for the special case of single-server queues in tandem.
Journal Article