This paper explores the behaviour of a Bulk Arrival Retrial Queue Model (BARQ) with two phases of service under the Bernoulli Vacation schedule and Breakdown (BVSB). Each batch of customers arriving the system finds if the server is available, instantly utilizes the service. If the server is busy, under breakdown, or taking a vacation, then the customers enter into the orbit. After completing both service stages, the server will either take a vacation with probability p or wait until the next customer arrives with probability 1 - p or q. Our approach considers the nature of the customer as balking and also takes into account the breakdown of server, which may occur instantaneously during any stage of service. Significant performance measures have been derived and presented. A numerical study of the proposed model is carried out using MATLAB and results were reported.
WuC.H. and YangD.Y., Bi-objective optimization of a queueing model with two-phase heterogeneous service, Computers & Operations Research (2021).
2.
KalitaC.R. and ChoudhuryG., An repeated service queue with N-policy and setup time subject to server’s breakdown and delayed repair, Communications in Statistics-Theory and Methods49(23) (2020), 5709–5737.
3.
RevathiC. and RajF., Search of arrivals of an M/G/1 retrial queueing system with delayed repair and optionalre-service using modified bernoulli vacation, J Comput Math6 (2022), 200–209.
4.
ArivudainambiD., GodhandaramanP. and RajaduraiP., Performance analysis of a single server retrial queue withworking vacation, Opsearch51 (2014), 434–462.
5.
ZiremD., BoualemM., Adel-AissanouK. and AïssaniD., Analysis of a single server batch arrival unreliablequeue with balking and general retrial time, Qual Technol Quant Manage16(6) (2019), 672–695.
6.
HaightF.A., Queueing with renzeging, Metrika2(1) (1959), 186–197.
7.
MaraghiF.A., MadanK.C. and Darby-DowmanK., Bernoulli schedule vacation queue with batch arrivals and randomsystem breakdowns having general repair time distribution, International Journal of Operational Research7 (2010), 240–256.
8.
KhanI.E. and ParamasivamR., Reduction in waiting time in an M/M/1/N encouraged arrival queue with feedback,balking and maintaining of reneged customers, Symmetry14 (2022).
9.
KeJ.C., LiuT.H., SuS. and ZhangZ.G., On retrial queue with customer balking and feedback subject to serverbreakdowns, Communications in Statistics-Theory and Methods51(17) (2022), 6049–6063.
10.
KeilsonJ. and ServiL.D., Oscillating random walk models for GI/G/1vacation systems with Bernoulli schedule, J Appl Probab23(3) (1986), 790–802.
11.
MedhiJ., A single server Poisson input queue with a second optional channel, Queueing Systems42(3) (2002), 239–242.
12.
JainM. and KaurS., Bernoulli vacation model for MX/G/1 unreliable server retrial queue with bernoulli feedback,balking and optional service, RAIRO-Operations Research55 (2021), S2027–S2053.
13.
LaxmiP.V., QrewH.A. and GeorgeA.A., Analyis of Markovian batch service queue with feedback and second optionalservice, Reliab.: Theory Appl17 (2022), 507–518.
14.
MadheswariS.P. and SuganthiP., Retrial queue with unreliable server and second optional service under K types of Bernoulli vacations, International Journal of Services and Operations Management40 (2021), 502–533.
15.
RaoS.S., Queueing with balking and reneging in M/G/1 systems, Metrika12 (1968), 173–188.
16.
GaoS., DongH. and WangX., Equilibrium and pricing analysis for an unreliable retrial queue with limited idleperiod and single vacation, Operational Research21(1) (2021), 621–643.
17.
GaoS., WangJ. and LiW., An M/G/1 retrial queue with general retrial times, working vacations and vacationinterruption, Asia-Pac J Oper Res31 (2014), 6–31.
18.
GaoS., ZhangJ. and WangX., Analysis of a retrial queue with two-type breakdowns and delayed repairs, IEEEAccess8 (2020), 172428–172442.
19.
NandhiniS. and PalaniammalS., Fuzzy based congestion detection technique for queuing in IP Networks, International Review on Computers and Software (IRESCOS)8(4) (2013).
20.
YangT., PosnerM.J.M. and TempletonJ.G.C., The M/G/1 retrial queuewith non-persistent customers, QueueingSystems7(2) (1990), 209–218.
21.
KulkarniV.G. and ChoiB.D., Retrial queues with server subject to breakdowns and repairs, Queueing Syst7 (1990), 191–208.
22.
XiaoyongW., BrillP., HlynkaM. and WangJ., An M/G/1 retrial queue with balking and retrials during service, International Journal of Operational Research1(1) (2005), 30–51.
