ANALYSIS OF PRIORITY QUEUEING SYSTEM WITH WORKING  BREAKDOWN, REPAIR, IMMEDIATE FEEDBACK AND BERNOULLI VACATION

G Ayyappan; B Somasundaram; J Udayageetha

doi:10.48165/

Authors

G Ayyappan Department of Mathematics, Pondicherry Engineering College, Puducherry, Tamil Nadu 605014, India
B Somasundaram Department of Mathematics, Pondicherry Engineering College, Puducherry, Tamil Nadu 605014, India
J Udayageetha Department of Mathematics, Perunthalaivar Kamarajar Arts College, Puducherry, Tamil Nadu 605107, India

DOI:

https://doi.org/10.48165/

Keywords:

Batch arrival, Priority queue, Working breakdow, Immediate feedback, Bernoulli vacation

Abstract

We analyze an [ ], [ ]/ ,/1 queue with two classes of non-preemptive priority service based on working breakdown, repair, immediate feedback and Bernoulli vacation. The server may subject to random breakdown with parameter , during high priority service (type I), then the server will complete the service for current customer at a slower service rate compared to the regular service rate. On the other hand, during low priority service (type II), it should go for repair immediately. After the completion of each high priority service, there are two choices. First, the server can go for vacation with probability , secondly, its serves the next customer which has the probability (1 − ). In case of customer dissatisfaction after completion of high priority service, immediately they receive service again without joining queue with probability , or else the customer gets an option to discard, which has a probability of (1 − ). We use the established norm, which is the corresponding steady state results for the time dependent probability generating functions. Along with that, the expected time of wait for the expected number of customers in the high and low priority queues are computed. Numerical results along with the graphical representations are shown elaborately.

References

. Ayyappan, G. and Shyamala, S. (2016). Transient solution of an [ ]/ /1 queueing model with feedback, random breakdowns, Bernoulli schedule server vacation and random setup time, International Journal of Operational Research, 25(2), 196-211.

. Baskar, S. and Palaniammal, S. (2013). A single server / /1 queue with preemptive repeat priority service with server vacation, Applied Mathematical Sciences, 7(94), 4651 - 4674.

. Choudhury, G. and Kalita, C. R. (2018). An / /1 queue with two types of general heterogeneous service and optional repeated service subject to server’s breakdown and delayed repair,Quality Technology Quantitative Management, 15(5), 622-654.

. Kalidass, K. and Kasturi, R. (2012). A queue with working breakdowns,Computers and Industrial Engineering, 63(4), 779-783.

. Kalidass, K. and Kasturi, R. (2014). A two phase service / /1 queue with a finite number of immediate Bernoulli feedbacks,Operations Research and Decision Theory, 51(2), 201-218. [6]. Kim, B. K and Lee, D.H.(2014). The / /1 queue with disasters and working breakdowns, Applied Mathematical Modelling, 38(5-6), 1788-1798.

. Krishnamoorthy, A. Pramod, P.K. and Chakravarthy, S.R. (2014). Queues with interruptions: a survey, An Official Journal of the Spanish Society of Statistics and Operations Research, 22(1), 290-320. [8]. Krishnamoorthy, A. and Manjunath, A.S. (2018). On queues with priority determined by feedback,Calcutta Statistical Association Bulletin, 70(1), 33-56.

. Madan, K.C. (1973). A priority queueing system with service interruptions,Statistica Neerwndica, 27(3), 115-123.

. Maraghi, F.A., Madan, K.C. and Dowman, K.D. (2010). Batch arrival queueing system with random breakdowns and Bernoulli schedule server vacations having general vacation time distribution, International Journal of Operational Research, 7(2), 240-256.

. Medhi, J. (2002). Stochastic models in queueing theory, Second edition, Academic Press, New York. [12]. Rajadurai, P. (2018). Sensitivity analysis of an / /1 retrial queueing system with disaster under working vacations and working breakdowns, RAIRO-Oper. Res., 52(1), 35-54.

. Saravanarajan, M.C. and Chandrasekaran, V.M. (2014). Analysis of / /1feedback queue with two types of services, Bernoulli vacations and random breakdown, Int. J. Mathematics in Operational Research, 6(5), 567-588.

. Senthil Kumar, M., Chakravarthy, S.R. and Arumuganathan, R. (2013). Preemptive resume priority retrial queue with two classes of MAP arrivals, Applied Mathematical Sciences, 7(52), 2569-2589. [15]. Takacs, L. (1963). A single server queue with feedback, The Bell System Technical Journal, 42, 487-503.