# SCS

## Seminar

### Semi-open problems in open and closed queueing networks

Seminar Room 1, Newton Institute

#### Abstract

In this talk we consider both a closed cyclic two-queue system and an open tandem two-queue system, consisting of a single server FCFS queue with general service time distribution and a single server FCFS queue with exponential service time distribution. For the closed cyclic system, the joint steady-state sojourn time distribution of a tagged customer visiting first the M queue and then the G queue was obtained in [2]. It is easily seen that this distribution is in general different from the joint steady-state sojourn time distribution in first the G queue and then the M queue; determination of the latter distribution has remained an open problem. The main goal of the talk is to demonstrate how that joint distribution can be obtained.The used methodology may have larger applicability; in the last part of the talk we shall discuss ongoing work on using the same method to determine the joint steady-state distribution of the sojourn times of a tagged customer in an M/G/1 FCFS queue followed by a ./M/1 FCFS queue. For the latter open tandem model, the joint steady-state queue length distribution has been obtained in [1] using a boundary value method.

References: 1. J.P.C. Blanc, R. Iasnogorodski and Ph. Nain (1988). Analysis of the M/GI/1 -> ./M/1 queueing model. Queueing Systems 3, 129-156. O.J. Boxma (1983). The cyclic queue with one general and one exponential server. Adv. Appl. Probab. 15, 857-873. Note: This is joint work with Hans Daduna

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