A queueing network approach to the module allocation problem in distributed systems
01 Sep 1981-Vol. 10, Iss: 3, pp 191-204
TL;DR: This paper discusses an alternative approach to the module allocation problem where a closed, multiclass queueing network is solved to determine the cost of a particular module allocation, and suggests that substantial problems of this type could be solved.
Abstract: Given a collection of distributed programs and the modules they use, the module allocation problem is to determine an assignment of modules to processors that minimizes the total execution cost of the programs. Standard approaches to this problem are based on solving either a network flow problem or a constrained 0-1 integer programming problem.In this paper we discuss an alternative approach to the module allocation problem where a closed, multiclass queueing network is solved to determine the cost of a particular module allocation. The advantage of this approach is that the execution cost can be expressed in terms of performance measures of the system such as response time. An interchange heuristic is proposed as a method of searching for a good module allocation using this model and empirical evidence for the success of the heuristic is given. The heuristic normally finds module allocations with costs within 10 percent of the optimal module allocation.Fast, approximate queueing network solution techniques based on mean-value-analysis allow each heuristic search to be completed in a few seconds of CPU time. The computational complexity of each search is O (M K (K + N) C) where M is the number of modules, K is the number of sites in the network, N is the number of communications processors, and C is the number of distributed program types. It appears that substantial problems of this type could be solved using the methods we describe.
Citations
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IBM1
TL;DR: An efficient algorithm to determine the mean completion time and related performance measures for a task system: a set of tasks with precedence relationships in their execution sequence, such that the resulting graph is acyclic.
Abstract: This paper is concerned with the performance evaluation of a realistic model of parallel computations. We present an efficient algorithm to determine the mean completion time and related performance measures for a task system: a set of tasks with precedence relationships in their execution sequence, such that the resulting graph is acyclic. A queueing network (QN) is used to model tasks executing on a single or multicomputer system. In the case of multicomputer systems, we take into account the delay due to interprocess communication. A straight- forward application of a QN solver to the problem is not possible due to variations in the state of the system (composition of tasks in execution). An accurate algorithm based on hierarchical decomposition is presented for solving task systems. At the higher level, the system behavior is specified by a Markov chain whose states correspond to the combination of tasks in execution. The state transition rate matrix for the Markov chain is triangular (since the task system graph was assumed to be acyclic), therefore it can be solved efficiently to compute the state probabilities and the task initiation/completion times. At the lower level, the transition rates among the states of the Markov chain are computed using a QN solver, which determines the throughput of the computer system for each system state. The model and the solution method can be used in performance evaluation of applications exhibiting concurrency in centralized/distributed systems where there are conflicting goals of load balancing and minimizing interprocess communication overhead.
115 citations
TL;DR: In this article, the problem of task allocation in fault-tolerant distributed systems is formulated as a constrained sum-of-squares minimization problem and an efficient approximation algorithm is proposed.
Abstract: This paper examines task allocation in fault-tolerant distributed systems. The problem is formulated as a constrained sum of squares minimization problem. The computational complexity of this problem prompts us to consider an efficient approximation algorithm. We show that the ratio of the performance of the approximation algorithm to that of the optimal solution is bounded by 9m/(8m?r+1)), wherem is the number of processors to be allocated andr is the number of times each task is to be replicated. Experience with the algorithm suggests that even better performance ratios can be expected.
113 citations
TL;DR: A branch-and-bound-with-underestimates algorithm to reduce the size of the search tree, and its average time and space complexity for two underestimating functions through simulation, which shows the minimum independent assignment cost underestimate (MIACU), performs extremely well over a wide range of values of program model parameters.
110 citations
05 Jan 1993
TL;DR: Hill-climbing, simulated annealing and genetic algorithms are search techniques that can be applied to most combinatorial optimization problems and are used to solve the mapping problem, which is the optimal static allocation of communication processes on distributed memory architectures.
Abstract: Hill-climbing, simulated annealing and genetic algorithms are search techniques that can be applied to most combinatorial optimization problems. The three algorithms are used to solve the mapping problem, which is the optimal static allocation of communication processes on distributed memory architectures. Each algorithm is independently evaluated and optimized according to its parameters. The parallelization of the algorithms is also considered. As an example, a massively parallel genetic algorithm is proposed for the problem, and results of its implementation on a 128-processor Supernode are given. A comparative study of the algorithms is then carried out. The criteria of performance considered are the quality of the solutions obtained and the amount of search time used for several benchmarks. A hybrid approach consisting of a combination of genetic algorithms and hill-climbing is also proposed and evaluated. >
67 citations
TL;DR: A distributed polynomial allocation algorithm for determining an instantaneous probabilistic optimal policy for task allocation is presented and an analytical solution to find the optimal effort levels for the agents is given.
38 citations
References
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TL;DR: Many of the network results of Jackson on arrival and service rate dependencies, of Posner and Bernholtz on different classes of customers, and of Chandy on different types of service centers are combined and extended in this paper.
Abstract: We derive the joint equilibrium distribution of queue sizes in a network of queues containing N service centers and R classes of customers. The equilibrium state probabilities have the general form: P(S) - Cd(S) $f_1$($x_1$)$f_2$($x_2$)...$f_N$($x_N$) where S is the state of the system, $x_i$ is the configuration of customers at the ith service center, d(S) is a function of the state of the model, $f_i$ is a function that depends on the type of the ith service center, and C is a normalizing constant. We consider four types of service centers to model central processors, data channels, terminals, and routing delays. The queueing disciplines associated with these service centers include first-come-first-served, processor sharing, no queueing, and last-come-first-served. Each customer belongs to a single class of customers while awaiting or receiving service at a service center but may change classes and service centers according to fixed probabilities at the completion of a service request. For open networks we consider state dependent arrival processes. Closed networks are those with no arrivals. A network may be closed with respect to some classes of customers and open with respect to other classes of customers. At three of the four types of service centers, the service times of customers are governed by probability distributions having rational Laplace transforms, different classes of customers having different distributions. At first-come-first-served type service centers the service time distribution must be identical and exponential for all classes of customers. Many of the network results of Jackson on arrival and service rate dependencies, of Posner and Bernholtz on different classes of customers, and of Chandy on different types of service centers are combined and extended in this paper. The results become special cases of the model presented here. An example shows how different classes of customers can affect models of computer systems. Finally, we show that an equivalent model encompassing all of the results involves only classes of customers with identical exponentially distributed service times. All of the other structure of the first model can be absorbed into the fixed probabilities governing the change of class and change of service center of each class of customers.
2,416 citations
IBM1
TL;DR: It is shown that mean queue sizes, mean waiting times, and throughputs in closed multiple-chain queuing networks which have product-form solution can be computed recursively without computing product terms and normalization constants.
Abstract: It is shown that mean queue sizes, mean waiting times, and throughputs in closed multiple-chain queuing networks which have product-form solution can be computed recursively without computing product terms and normalization constants. The resulting computational procedures have improved properties (avoidance of numerical problems and, in some cases, fewer operations) compared to previous algorithms. Furthermore, the new algorithms have a physically meaningful interpretation which provides the basis for heuristic extensions that allow the approximate solution of networks with a very large number of closed chains, and which is shown to be asymptotically valid for large chain populations.
1,192 citations
TL;DR: This paper shows that this program module assignment problem can be solved efficiently by making use of the well-known Ford–Fulkerson algorithm for finding maximum flows in commodity networks as modified by Edmonds and Karp, Dinic, and Karzanov.
Abstract: In a distributed computing system a modular program must have its modules assigned among the processors so as to avoid excessive interprocessor communication while taking advantage of specific efficiencies of some processors in executing some program modules. In this paper we show that this program module assignment problem can be solved efficiently by making use of the well-known Ford–Fulkerson algorithm for finding maximum flows in commodity networks as modified by Edmonds and Karp, Dinic, and Karzanov. A solution to the two-processor problem is given, and extensions to three and n-processors are considered with partial results given without a complete efficient solution.
740 citations
TL;DR: This tutorial paper presents the basic results using the operational approach, a framework which allows the analyst to test whether each assumption is met in a given system, and methods for computing basic performance quantities.
Abstract: Queueing network models have proved to be cost effectwe tools for analyzing modern computer systems. This tutorial paper presents the basic results using the operational approach, a framework which allows the analyst to test whether each assumption is met in a given system. The early sections describe the nature of queueing network models and their apphcations for calculating and predicting performance quantitms The basic performance quantities--such as utilizations, mean queue lengths, and mean response tunes--are defined, and operatmnal relationships among them are derwed Following this, the concept of job flow balance is introduced and used to study asymptotic throughputs and response tunes. The concepts of state transition balance, one-step behavior, and homogeneity are then used to relate the proportions of time that each system state is occupied to the parameters of job demand and to dewce charactenstms Efficmnt methods for computing basic performance quantities are also described. Finally the concept of decomposition is used to stmphfy analyses by replacing subsystems with equivalent devices. All concepts are illustrated liberally with examples
587 citations
TL;DR: This perspective exposes the further research which is necessary in order to provide a truly satisfactory solution to the file assignment problem.
Abstract: The optimal distribution of files among storage nodes is a major problem m computer system optimization. Differing design goals, varying system assumptions, and contrasting solution techniques yield a disparity of optimal file assignments. This paper views the differing file assignment models in a uniform manner Relative advantages and weaknesses of the various models become immediately apparent. This perspective exposes the further research which is necessary m order to provide a truly satisfactory solution to the file assignment problem
538 citations