ON THE INFINITE SERVER SHORTEST QUEUE PROBLEM: SYMMETRIC CASE

Abstract

We consider two identical parallel M/M/∞ queues. A new arrival is routed to the queue with the smaller number of customers. If both systems have equal occupancy, the arrival joins either with probability 1/2. These types of models have been used to describe CDMA (Code Division Multiple Access) cellular systems. We analyze this model both numerically and asymptotically. For the latter, we consider the limit ρ = λ/μ → ∞, where λ (resp., μ) is the arrival (resp., service) rate. An efficient numerical method is developed for computing the joint steady-state distribution of the number of customers in the two queues. We give several asymptotic formulas, valid for different ranges of the state variables, which show the qualitative structure of the joint distribution. The numerical accuracy of the asymptotic results is tested.

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