This paper investigate a queueing model where in customers arrive in batches according to compound Poisson process with rate λ and are served one by one in FIFO basis. All incoming customers demand the first ’essential’ service wherein only some of them demand the second ’optional’ service. The service times of both essential and optional services follow arbitrary(general)distribution with diff...

An M x /G/1 queueing system with second optional service (SOS)is studied under N policy and Bernoulli Vacation. The system remains idle until the queue size reaches or exceeds N ( ≥ 1). When the queue size reaches at leastN, the server may begin his setup operation with probability s or may start the service with probability (1-s). The server provides two phases of heterogeneous services, of wh...

We consider an M/G/1 queue with regular and optional phase vacation and withstate dependent arrival rate. The vacation policy is after completion of service if there are no customers in the system, the server takes vacation consisting of K -phases, each phase is generally distributed. Here the first phase is compulsory where as the other phases are optional. For this model the supplementary var...

In this paper, a bulk arrival retrial queueing model with two phases of service symbolically denoted by M/(G1,G2)/1 has been discussed under Bernoulli vacation schedule to explore main ly its steady state behaviour using maximum entropy principle (MEP). We consider that customers arrive in batches according to Poisson distribution and a single server of the system provides his services in two p...

This paper aims to investigate M[X]/(G1, G2)/1/VAC(J) queuing system with a random(p) vacation policy and optional second service, where X is the batch arrival number of customers. When no customers are in system, server immediately goes on vacation. And when returns from finds that at least one customer waiting will provide First Essential Service (FES). After complete first essential some con...

Multi-server retrial queue with second optional service: algorithmic computation and optimisation Jau-Chuan Ke a , Chia-Huang Wu b & Wen Lea Pearn b a Department of Applied Statistics , National Taichung Institute of Technology , No. 129, Sec. 3, Sanmin Road, Taichung, Taiwan 404, ROC b Department of Industrial Engineering and Management , National Chiao Tung University , Hsinchu, Taiwan 300, R...

We consider a discrete-time Geo/G/1 retrial queue with starting failures in which all the arriving customers require a first essential service while only some of them ask for a second optional service. We study the Markov chain underlying the considered queueing system and its ergodicity condition. Explicit formulae for the stationary distribution and some performance measures of the system in ...