Home List of Titles Positive Harris recurrence and diffusion scale analysis of a push pull queueing network
Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.3/158853
- Positive Harris recurrence and diffusion scale analysis of a push pull queueing network
- Nazarathy, Yoni; Weiss, Gideon
- We consider a push pull queueing network with two servers and two types of job which are processed by the two servers in opposite order, with stochastic generally distributed processing times. This push pull network was introduced by Kopzon and Weiss, who assumed exponential processing times. It is similar to the Kumar-Seidman Rybko-Stolyar (KSRS) multi-class queueing network, with the distinction that instead of random arrivals, there is an infinite supply of jobs of both types. Unlike the KSRS network, we can find policies under which our push pull network works at full utilization, with both servers busy at all times, and without being congested. We perform fluid and diffusion scale analysis of this network under such policies, to show fluid stability, positive Harris recurrence, and to obtain a diffusion limit for the network. On the diffusion scale the network is empty, and the departures of the two types of job are highly negatively correlated Brownian motions. Using similar methods we also derive a diffusion limit of a re-entrant line with an infinite supply of work.
- Publication type
- Journal article
- Performance Evaluation: selected papers from the 3rd International Conference on Performance Evaluation Methodologies and Tools (VALUETOOLS 2008), Athens, Greece, 20-24 October 2008, Vol. 67, no. 4 (Apr 2010), pp. 201-217
- Publication year
- FOR Code(s)
- 01 Mathematical Sciences; 08 Information and Computing Sciences; 10 Technology
- Brownian movement; Diffusion; Diffusion limits; Fluid models; Fluids; Infinite virtual queues; Petite bounded sets; Plasma flow; Positive Harris recurrence; Push pull; Queueing networks; Queueing theory; Statistics; Virtual queue
- Publisher URL
- Copyright © 2009 Elsevier B.V. All rights reserved.
- Peer reviewed