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

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.