Markovian queueing systems with retrials and heterogeneous servers

✍ Scribed by B. Pourbabai

• Publisher: Elsevier Science
• Year: 1987
• Tongue: English
• Weight: 410 KB
• Volume: 13
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/0898-1221(87)90064-2

✦ Synopsis

The asymptotic performances of a random access and an ordered entry G/M/K/O queueing system with a stationary counting arrival process, K heterogeneous parallel servers, no waiting room and retrials are approximated based on a two-parameter method. In a random access system, units upon arrival are randomly assigned to one of the servers. In an ordered entry system, servers are indexed from I to K, and units first arrive at server i and if the server is found to be busy, those units arrive at server (i + 1), for i --1 to K -1. In both queueing systems, if units are not processed by one of the servers, those units are not lost, instead they retry to receive service by merging with the incoming arrival units.

To approximate the asymptotic performance of the above queueing systems, a recursive algorithm is suggested, and appropriate performance measures are presented to be used as comparison criteria at the design stage. Furthermore, numerical results are provided and approximation outcomes are compared against those from a simulation study.