Performance analysis of an M/G/1 queueing system under Bernoulli vacation schedules with server setup and close down periods

• Published in: Computers & industrial engineering 2013-09, Vol.66 (1), p.1-9
• Main Authors: Krishna Kumar, B., Rukmani, R., Anantha Lakshmi, S.R.
• Format: Article
• Language: English
• Subjects: Bernoulli vacations; Imbedded Markov chain; Laplace transforms; Markov analysis; Mathematical functions; Probability distribution; Probability generating function; Queuing theory; Setup and close down periods; Studies; System size; Vacations; Waiting time
• ISSN: 0360-8352; 1879-0550
• DOI: 10.1016/j.cie.2013.06.005

•A non-Markovain queueing model with Bernoulli vacation subject to server setup and close down period is analyzed.•Explicit expression for probability generating function of the system size is obtained.•Steady-state probabilities and LST of waiting time distribution are derived.•The standard performance measures are obtained.•The effect of the system parameters on the performance measures are illustrated numerically. This paper is concerned with the analysis of a single server queueing system subject to Bernoulli vacation schedules with server setup and close down periods. An explicit expression for the probability generating function of the number of customers present in the system is obtained by using imbedded Markov chain technique. The steady state probabilities of no customer in the system at the end of vacation termination epoch and a service completion epoch are derived. The mean number of customers served during a service period and the mean number of customers in the system at an arbitrary epoch are investigated under steady state. Further, the Laplace-Stieltjes transform of the waiting time distribution and its corresponding mean are studied. Numerical results are provided to illustrate the effect of system parameters on the performance measures.