Volume 55, 2021Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|Page(s)||S225 - S251|
|Published online||09 February 2021|
A single server queue under random vacation policy
Mathematical Sciences Division, Institute of Advanced Study in Science and Technology, 781035, Guwahati, Assam, India.
* Corresponding author: firstname.lastname@example.org
Accepted: 6 September 2019
This paper deals with an M/G/1 queueing system with random vacation policy, in which the server takes the maximum number of random vacations till it finds minimum one message (customer) waiting in a queue at a vacation completion epoch. If no arrival occurs after completing maximum number of random vacations, the server stays dormant in the system and waits for the upcoming arrival. Here, we obtain steady state queue size distribution at an idle period completion epoch and service completion epoch. We also obtain the steady state system size probabilities and system state probabilities. Some significant measures such as a mean number of customers served during the busy period, Laplace-Stieltjes transform of unfinished work and its corresponding mean value and second moment have been obtained for the system. A cost optimal policy have been developed in terms of the average cost function to determine a locally optimal random vacation policy at a lower cost. Finally, we present various numerical results for the above system performance measures.
Mathematics Subject Classification: 60K25 / 90B22 / 60K20
Key words: M/G/1 queue / Random vacation policy / embedded Markov chain / Markov regenerative process / cost optimal policy
© EDP Sciences, ROADEF, SMAI 2021
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