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

Subject Areas : International Journal of Mathematical Modelling & Computations

P. Vijaya Laxmi ¹ , K. Jyothsna ²

1 - Department of Applied Mathematics, Andhra University, Visakhapatnam 530003, India.
2 - Department of Applied Mathematics, Andhra University, Visakhapatnam 530003, India.

Received: 2016-07-13 Accepted : 2016-07-13 Published : 2016-03-01

Keywords: particle swarm optimization, discrete-time, balking, Reneging, Bernoulli-schedule vacation interruption,

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.

References:

[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.