MATHEMATICAL SCIENCES AND APPLICATIONS E-NOTES
VOLUME 3 NO. 2, PP. 34-44 (2015) @MSAEN
ON a QUEUEING SYSTEM WITH GENERALIZED COXIAN-2 SERVICE AND OPTIONAL GENERALIZED COXIAN-2 VACATION
Prof. Kailash C. Madan
Ahlia University, Bahrain
Abstract. We study the steady state behaviour of a batch arrival single server queue in which the first service with general service times is compulsory and the second service with general service times is optional. We term such a two phase service as generalized Coxian-2 service. Just after completion of a service the server may take a vacatiosn of random length of time with general vacation times . After completion of the first phase of vacation the server may or may not take the second optional vacation with general vacation times . We term this two phase vacation as optional generalized Coxian-2 sever vacation. We obtain steady state probability generating functions for the queue size at a random epoch of time in explicit and closed forms. Some particular cases of interest including some known results have been derived.
2010 Mathematics Subject Classification. 60 K:25.
Key words and phrases. Batch arrivals, generalized Coxian-2 service, generalized Coxian-2 vacation, steady stat
Date: Received: October 08, 2014; Revised: June 06, 2015; Accepted: July 1, 2015.
This article is the written version of author’s plenary talk delivered on August 25-28, 2014 at 3rd International Eurasian Conference on Mathematical Sciences and Applications IECMSA-2014 at Vienna, Austria.
AuthorE-Mails:
kmadan@ahlia.edu.bh
kcmadan@yahoo.com