ANALYSIS OF A DISCRETE-TIME IMPATIENT CUSTOMER QUEUE WITH BERNOULLI-SCHEDULE VACATION INTERRUPTION

Authors

Department of Applied Mathematics, Andhra University, Visakhapatnam 530003, India.

Abstract

This paper investigates a discrete-time impatient customer queue with Bernoulli-schedule vacation interruption. The  vacation times and the service times during regular busy period and during working vacation period are assumed to follow geometric distribution. We obtain the steady-state probabilities at arbitrary and outside observer's observation epochs using recursive technique. Cost analysis is carried out using particle swarm optimization.  Computational experiences with a variety of numerical results are discussed.

Keywords


[1] V. Goswami, Analysis of discrete-time multi-server queue with balking, Int. J. Manage. Sci. Eng.
Manage, 9 (1) (2014) 21–32.
[2] V. Goswami, A discrete-time queue with balking, reneging and working vacations, Int. J. Stoch.
Anal., Article ID 358529, http://dx.doi.org/10.1155/2014/358529,(2014).
[3] M. Lozano and P. Moreno, A discrete time single-server queue with balking: economic applications,
Appl. Econ, 40 (6) (2008) 735–748.
[4] S. S. Rao, Engineering Optimization: Theory and Practice, John Wiley & Sons, Hoboken, New
Jersey, USA, (2009).
[5] L. D. Servi and S. G. Finn, M/M/1 queues with working vacations (M/M/1/W V ), Perf. Eval, 50
(1) (2002) 41–52.
[6] N. Tian, Z. Ma and M. Liu, The discrete time Geom/Geom/1 queue with multiple working vacations,
Appl. Math. Model, 32 (12) (2008) 2941–2953.
[7] P. Vijaya Laxmi, V. Goswami and K. Jyothsna, Analysis of finite buffer Markovian queue with
balking, reneging and working vacations, Int. J. Strat. Dec. Sci, 4 (1) (2013) 1–24.
[8] P. Vijaya Laxmi and K. Jyothsna, Impatient customer queue with Bernoulli schedule vacation interruption,
Comput. Oper. Res, 56 (2015) 1–7.
[9] H. Zhang and D. Shi, The M/M/1 queue with Bernoulli-schedule-controlled vacation and vacation
interruption, Int. J. Inform. Manage. Sci, 20 (2009) 579–587.