The Power-Series Algorithm Applied to the Shortest-Queue Model

J.P.C. Blanc

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

Abstract

An iterative numerical technique for the evaluation of queue length distribution is applied to multiserver systems with queues in parallel in which customers join (one of) the shortest queues upon arrival. The technique is based on power-series expansions of the state probabilities as functions of the load of the system. The convergence of the series is accelerated by applying a modified form of the epsilon algorithm. The shortest-queue model lends itself particularly well to a numerical analysis by means of the power-series algorithm due to a specific property of this model. Numerical values for the mean and the standard deviation of the total number of customers and the waiting times in stationary symmetrical systems are obtained for practically all values of the load for systems with up to ten queues and for a load not exceeding 75% for systems with up to 30 queues. Data are also presented for systems with four queues and unequal service rates.

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References

1986Term Structure Movements and Pricing Interest Rate Contingent Claims 1961Two Similar Queues in Parallel 1988Jump-Diffusion Processes and the Term Structure of Interest Rates 1972A Dynamic Model for Bond Portfolio Management 1978An arbitrage model of the term structure of interest rates 1977Two queues in parallel 1970Financial market rates and flows 1985The shortest queue problem

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