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May, 1994 Instability of FIFO Queueing Networks
Maury Bramson
Ann. Appl. Probab. 4(2): 414-431 (May, 1994). DOI: 10.1214/aoap/1177005066


Consider a queueing network with customers arriving according to a rate-1 Poisson process. Each customer proceeds along the same prescribed route, waiting at the different queues until exiting from the system. The service times are assumed to be independent and exponentially distributed. Individual queues may be visited more than once by a customer, with the mean service time perhaps depending on the stage along the route. The network is assumed to be first-in, first-out. An obvious necessary condition for such a queueing network to have an equilibrium distribution is that the sum of the mean service times at each queue be less than 1. We show by means of a class of examples that this condition does not suffice, these networks being unstable. Each such network possesses two queues, the first with one slow and one quick stage, and the other with one slow and numerous quick stages.


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Maury Bramson. "Instability of FIFO Queueing Networks." Ann. Appl. Probab. 4 (2) 414 - 431, May, 1994.


Published: May, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0804.60079
MathSciNet: MR1272733
Digital Object Identifier: 10.1214/aoap/1177005066

Primary: 60K25
Secondary: 68M20

Keywords: equilibrium distribution , first-in , first-out , instability , Queueing networks

Rights: Copyright © 1994 Institute of Mathematical Statistics


Vol.4 • No. 2 • May, 1994
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