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This article analyses a bulk queueing system with multiple vacations, controlled arrival and breakdown. The service is done in bulk with a minimum of 'a' customers and a maximum of 'b' customers. The server is assigned for secondary jobs (vacations) repeatedly when the number of customers is inadequate to process. The arrivals are accepted with a probability α, β and γ during the busy, vacation and renovation period respectively. During a batch service, if the server breaks down with probability π, the service for the particular batch is processed without interruption. Upon completion of service, the renovation of service station will be considered. The probability generating function for the queue size at an arbitrary time epoch is derived. Various performance measures are obtained. A few particular cases are discussed. Maximum entropy analysis is carried out and validated through numerical illustration. The cost model is also developed to optimise the cost.

In this paper, a batch arrival single server queuing system with startup, balking and vacation interruption is considered. During the busy period, the customers may join the queue with probability α or may balk with probability 1−. On completion of service, the server goes for vacation when there are no customers available in the queue, otherwise, it resumes service. After a vacation, the server stays idle until the customer arrives and when an arrival occurs, the server begins the startup followed by service. Furthermore, vacation is interrupted suddenly when a customer arrives during vacation and goes for startup and then starts service. The probability generating function of the system size at an arbitrary time epoch is obtained. Various performance measures, some particular cases and cost model are discussed. Moreover, maximum entropy approach is employed and the results are compared with the analytical results, and validated through numerical illustration.

In this paper, a batch arrival single server retrial queue with modified vacations under N -policy is considered. If an arriving batch of customers finds the server busy or on vacation, then the entire batch joins the orbit in order to seek the service again. Otherwise, one customer from the arriving batch receives the service, while the rest joins the orbit. The customers in the orbit will try for service one by one when the server is idle with a classical retrial policy with the retrial rate ‘jv ’, where ‘j ’ is the size of the orbit. At a service completion epoch, if the number of customers in the orbit is zero, then the server leaves for a secondary job (vacation) of random length. At a vacation completion epoch, if the orbit size is at least N , then the server remains in the system to render service for the primary customers or orbital customers. On the other hand, if the number of customers in the orbit is less than ‘N ’ at a vacation completion epoch, the server avails multiple vacations subject to maximum ‘M ’ repeated vacations. After availing ‘M ’ consecutive vacations, the server returns to the system to render service irrespective of the orbit size. The model is studied using supplementary variable technique. For the proposed queueing system, the probability generating function of the steady state queue size distribution at an arbitrary time is obtained. Various performance measures are derived. A cost model for the queueing system is developed. Numerical illustration is provided.

In this paper, a batch arrival general bulk service queueing system with interrupted vacation (secondary job) is considered. At a service completion epoch, if the server finds at least ‘a ’ customers waiting for service say ξ , he serves a batch of min (ξ , b) customers, where b ≥ a . On the other hand, if the queue length is at the most ‘a -1’, the server leaves for a secondary job (vacation) of random length. It is assumed that the secondary job is interrupted abruptly and the server resumes for primary service, if the queue size reaches ‘a ’, during the secondary job period. On completion of the secondary job, the server remains in the system (dormant period) until the queue length reaches ‘a ’. For the proposed model, the probability generating function of the steady state queue size distribution at an arbitrary time is obtained. Various performance measures are derived. A cost model for the queueing system is also developed. To optimize the cost, a numerical illustration is provided.

In this paper, a bulk queueing system with server’s choice of admitting reservice, multiple vacations and setup time is considered. At a service completion, the leaving batch may request for reservice with probability ʌ and it is not mandatory to accept it; the server admits this request with a probability α. After the reservice or service completion without request for reservice, if the queue length is less than a, the server leaves for a vacation of random length. After this vacation, if the queue length is still less than ‘a’, the server leaves for another vacation, etc., until he finally finds at least ‘a’ customers waiting for service. At a vacation completion epoch, if the server finds at least ‘a’ customers waiting for service, he requires a setup time to start the service. After a setup time or on service completion or on reservice completion, if the server finds at least ‘a’ customers waiting for service say, [ he serves a batch of min (ξ, b) customers, where t ba. The probability generating func...

This paper studies a batch arrival general bulk service retrial queueing model with constant retrial rate. The primary customers arrive in bulk according to Poisson process and they get service under general bulk service rule with minimum of one customer and maximum of ‘b’ customers. If the arriving batch of customers, of size ‘ζ ’, 1≤ζ ≤ b , finds the server free, then all of them get service immediately; while, if the size of the arriving batch is more than ‘b’, then, ‘b’ customers enter the service station and the remaining ζ - b customers join the orbit. However, if an arriving batch of customers finds the server busy, then the entire batch joins the orbit in order to seek service again. The customers in the orbit will try for service one by one with a constant retrial rate ‘v’ when the server is idle. For the proposed model, the probability generating function of the steady-state queue size distribution at an arbitrary time, expected number of customers in the orbit, expected waiting time, expected length of busy period and expected length of busy cycle are obtained. The cost analysis of the queueing system is discussed. The effects of several parameters on the system are analysed numerically.