M/M/1 QUEUE WITH BREAKDOWNS, TWO VARIETIES OF REPAIR FACILITIES, TIMEOUT AND VACATION

Authors:

Y. Saritha,V. N. Rama Devi,K. Chandan,

DOI NO:

https://doi.org/10.26782/jmcms.2020.07.00017

Keywords:

Vacation queuing system, two varieties of Repair facilities and timeout,breakdowns, length of the system,

Abstract

This paper details anM/M/1 system with breakdowns, two varieties of repair facilities, timeout and vacation. As soon as the system is vacant, the server pauses for a period 'c'. If no unit arrives at this time, the server get-away otherwise instigate the service to all the customers who gets in. There will be no delay in repair if the system breaks down as it is aided with two varieties of Repair facilities (TRF) based on the stage of service where it has failed. More clearly repair of Type-1 will be started with a chance of 1-q if the server fails atamidst of service and the other type is started with a likelihood q if failurehappens before the staring of service”. Various constants are derived and also done sensitivity analysis.

Refference:

I Doshi, B.T (1986), Queuing system with vacations. A survey on queuing system: Theory and Applications. 1(1), 29-66.
II GeniGupur, (2010), Analysis of the M/G/1 retrial Queuing Model with server breakdowns. Oper. 1:313-340.
III H.White and L. Christie. (1958),Queuing with preemptive priorities or with breakdown. Operations System, vol. 6(1), 79-95.
IV K.C. Madan, (2003), An M/G/1 type queue with Time-Homogeneous Breakdowns and Deterministic Repair Times, Soochow Journal of Mathematics Volume 29, No. 1, pp. 103110..
V Levy.Y and Yechiali. U, (1975), Utilization of Idle Time in an M/G/1 Queuing System. Management Science, 22, 202-211. http://dx.doi.org/10.1287/mnsc.22.2.202.
VI Oliver C. Ibe (2007) Analysis and optimization of M/G/1 Vacation Queuing Systems with Server Timeout, Electronic Modeling, V.29, no. 4, ISSN 0204-3572.
VII S.Bama, M.I.Afthab Begum and P.Fijy Jose, (2015), Unreliable MX/G/1 queueing system with two types of Repair. International Journal of Innovative Research & Development, Vol. 4, No. 10, pp. 25-38.
VIII Y.Saritha, V.N. Rama Devi and K.Chandan (2020), M/G/1 Queue with Vacation, Two Cases of Repair Facilities and Server Timeout.TEST Engineering and Management,Vol.82,pp. 16358 – 16363.

View Download