Abstract
We provide two examples of strictly subcritical multiclass queueing networks which are unstable under the shortest remaining processing time (SRPT) service protocol. Both of them are reentrant lines with two servers and eight customer classes. The customer service times in our first system are deterministic, yielding an example of an unstable shortest remaining expected processing time (SERPT) network. In the second one, the service times in one customer class are randomized. Both our examples show also system instability under the shortest job first (SJF) discipline. A simulation study of robustness of our results with respect to changes in the customer interarrival and service times is also provided. Our results indicate that size-based service policies may not use the available resources efficiently in a multiserver network setting and in fact cause instability effects. This is in sharp contrast with their satisfactory performance for single-server queues.
Highlights
Following Serfozo [40], by a stochastic network we mean a system in which customers move among stations where they receive services; there may be queueing for services, Queueing Systems and customer routing and service times may be random
We provide two examples of strictly subcritical multiclass queueing networks which are unstable under the shortest remaining processing time (SRPT) service protocol
As an illustration of this fact, we provide an example of a similar unstable SRPT system, with the same network topology, in which the service times in one of the customer classes are randomized
Summary
Following Serfozo [40], by a stochastic network we mean a system in which customers move among stations where they receive services; there may be queueing for services,. It was found that even strictly subcritical FIFO queueing networks might be unstable Examples of such systems were given by Seidman [39] and Bramson [9,10] in the deterministic and random case, respectively. In the context of multiclass queueing networks, Banks and Dai [5] provided a simulation study demonstrating that a three station reentrant line with nine customer classes can be unstable under the SERPT protocol. Together with the findings of [32,41], our results indicate that size-based service policies may not use the available resources efficiently in a multiserver network setting and cause instability effects This is in sharp contrast with their satisfactory performance for single-server queues.
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