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.

This paper deals with the analysis of large-scale closed queueing network (QN) models which are used for the performance analysis of computer communication networks (CCN's). The computer systems are interconnected by a wide-area network. Users accessing local/remote computers are affected by the contention (queueing delays) at the computer systems and the communication subnet. The computational cost of analyzing such models increases exponentially with the number of user classes (chains), even when the QN is tractable (product-form). In fact, the submodels of the integrated model are generally not product-form, e.g., due to blocking at computer systems (multiprogramming level constraints) and in the communication subnet (window flow control constraints). Two approximate solution methods are proposed in this paper to analyze the integrated QN model. Both methods use decomposition and iterative techniques to exploit the structure of the QN model such that computational cost is proportional to the number of chains. The accuracy of the solution methods is validated against each other and simulation. The model is used to study the effect that channel capacity assignments, window sizes for congestion control, and routing have on system performance.

Queueing Network Models - QNM's with population size constraints and delayed blocked customers occur due to MultiProgramming Level - MPL constraints in computer systems and window flow-control mechanisms in Computer Communication Networks - CCN's. The computational cost of existing algorithms is unacceptable for large numbers of chains and high population sizes. A fast approximate solution technique based on load concealment is presented to solve such QNM's. The solution procedure is non-iterative in the case of fixed rate Poisson arrivals, while iteration is required in the case of quasi-random arrivals. Each iteration requires the solution of a single chain network of queues comprised of stations visited by each chain. We then present an algorithm to detect saturated chains and determine their maximum throughput. A fast solution algorithm due to Reiser for closed chains is also extended to the case of quasi-random arrivals. The accuracy of the proposed solution techniques is compared to previous techniques by applying it to a test case, reported in the literature, and a set of randomly generated examples.