 This paper deals with batch arrival unreliable queue with two phases of service and vacation under Bernoulli vacation schedule, which consist of a breakdown period and a delay period. For this model, we first derive the joint distribution of state of the server and queue size, which is one of the chief objectives of this paper. Secondly, we derive the pgf of the stationary queue size distribu...

In this paper we consider M[X]/G(a, b)/1 queueing system with accessible service, server breakdown without interruption, multiple vacation and closedown time. The service rule is as follows: the server starts service only when a minimum number of customers ′a′ is available in the queue and the maximum service capacity is ′b′ units such that late entries are allowed to join a service batch, with...

In this paper a single server preemptive priority queuing system consisting of two types of customer units with Poisson arrival, exponential service time distribution and exponential vacation is analyzed. Two type of customer units of which higher priority units of unlimited Poisson input are served by bulk service rule and limited Poisson input of low priority units served singly. The bulk ser...

Using an elegant transform domain iterative operator approach exhaustive fluid vacation models with strictly negative fluid rate during service has been analyzed, recently. Unfortunately, the potential presence of positive fluid rate during service (when the fluid input rate is larger than the fluid service rate) inhibits the use of all previously applied methodologies and makes the extension o...

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...

A single-server queueing system of MX/G/1 type with unlimited buffer size is considered. Whenever the system becomes empty, the server takes a single compulsory vacation that is independent of the arrival process. The service of the first customer after the vacation is preceded by a random setup time. We distinguish two cases of the evolution of the system: when the setup time begins after the ...

In this paper, we investigate a single server batch arrival non-Markovian retrial queueing model with random break down and Bernoulli vacation. Customers arrive in batches accordingly Poisson process with arrival rate λ but are served one by one with first come first served basis. All customers demand the first essential service, whereas only some of them demand the second optional service. The...

 Abstract—This paper considers a Geo/G/1 queue, in which the server operates a single vacation at end of each consecutive service period. After all the customers in the system are served exhaustively, the server immediately leaves for a vacation. Upon returning from the vacation, the server inspects the queue length. If there are customers waiting in the queue, the server either resumes servin...

This paper examines the operating characteristics of an M/G/1 retrial queueing system under Bernoulli vacation schedule with setup times. The server renders first phase of essential service (FPS) to all the arriving units whereas second phase of multi-optional services (SPS) to only some of them who demand for the same. The server may breakdown according to Poisson process in working state i.e....

In this paper, we considered a batch arrival feedback retrial queue with two phase of service under Bernoulli vacation schedule and orbit search. At the arrival epoch of a batch, if the server is busy, under repair or on vacation then the whole batch joins the orbit. Where as if the server is free, then one of the arriving customers starts his service immediately and the rest join the orbit. At...