An explicit solution to a tandem queueing model

Authors:
Charles Knessl
Affiliations:
Department of Mathematics, Statistics and Computer Science (M/C 249), University of Illinois at Chicago, Chicago, IL 60607, USA
Venue:
Queueing Systems: Theory and Applications
Year:
1998

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Abstract

We consider two queues in tandem, each with an exponential server, and with deterministic arrivals to the first queue. We obtain an explicit solution for the steady state distribution of the process (N_1(t), N_2(t), Y(t)), where N_j(t) is the queue length in the jth queue and Y(t) measures the time elapsed since the last arrival. Then we obtain the marginal distributions of (N_1(t), N_2(t)) and of N_2(t). We also evaluate the solution in various limiting cases, such as heavy traffic.