Details

Autor(en) / Beteiligte

• Devos, Arnaud
• Walraevens, Joris
• Fiems, Dieter
• Bruneel, Herwig

Titel

Heavy-Traffic Comparison of a Discrete-Time Generalized Processor Sharing Queue and a Pure Randomly Alternating Service Queue

Ist Teil von

• Mathematics (Basel), 2021-11, Vol.9 (21), p.2723

Ort / Verlag

Basel: MDPI AG

Erscheinungsjahr

2021

Quelle

EZB Electronic Journals Library

Beschreibungen/Notizen

• This paper compares two discrete-time single-server queueing models with two queues. In both models, the server is available to a queue with probability 1/2 at each service opportunity. Since obtaining easy-to-evaluate expressions for the joint moments is not feasible, we rely on a heavy-traffic limit approach. The correlation coefficient of the queue-contents is computed via the solution of a two-dimensional functional equation obtained by reducing it to a boundary value problem on a hyperbola. In most server-sharing models, it is assumed that the system is work-conserving in the sense that if one of the queues is empty, a customer of the other queue is served with probability 1. In our second model, we omit this work-conserving rule such that the server can be idle in case of a non-empty queue. Contrary to what we would expect, the resulting heavy-traffic approximations reveal that both models remain different for critically loaded queues.