Minimizing loss probability in queuing systems with heterogeneous servers

Saglam V., Shahbazov A.

IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE, vol.31, no.A2, pp.199-206, 2007 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 31 Issue: A2
  • Publication Date: 2007
  • Journal Name: IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.199-206
  • Keywords: service rate, Erlang's loss formula, heterogeneous servers, loss probability, recurrent input, exponential server, overflow distribution, EXTENSION, FORMULA, QUEUES, TIMES
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

The probabitity of losing a customer in M/G/n/0 and GI/M/n/0 loss queuing systems with heterogeneous servers is minimized. The first system uses a queue discipline in which a customer who arrives when there are free servers chooses any one of them with equal probability, but is lost otherwise. Provided that the sum of the servers rates are fixed, loss probability in this system attains minimum value when all the service rates are equal. The second system uses queue discipline, in which a customer who enters into the system is assigned to the server with the lowest number. Loss probability in this system takes the minimum value in the case when the fastest server rule is used in which an incoming customer is served by the free server with the shortest mean service time. If the mean of the arrival distribution is fixed, then loss probability is minimized by deterministic arrival distribution.