Abstract Imagine, you enter a grocery store to buy food. How many people do overlap with in this store? much time each person the In paper, we answer these questions by studying times between customers infinite server queue. We compute closed form steady-state distribution of pair and number that an arriving customer will with. Finally, define residual process counts overlapping queue for at le...

In this paper, by considering an $$M|M|1|\infty$$ queueing model, Bayes estimators of traffic intensity and system performance measures are discussed under (i) squared error loss function (SELF) (ii) entropy (ELF) (iii) LINEX with Beta prior. Further, minimum posterior risk associated obtained SELF. The the model compared Uniformly Minimum Variance Unbiased Estimators (UMVUEs) through simulation.

In this paper, we develop a general framework to analyze polling systems with either the autonomous-server or the time-limited service discipline. According to the autonomous-server discipline, the server continues servicing a queue for a certain period of time. According to the time-limited service discipline, the server continues servicing a queue for a certain period of time or until the que...

In this paper, we consider a multi-server queuing system in which additional servers are allowed for a longer queue to reduce the customer’s balking and reneging behavior. The customers are assumed to arrive in Poisson fashion and their service- times follow exponential distribution. The number of servers in long run depends on the queue-length. We obtain equilibrium queue size distribution. Th...

The M/M/1 retrial queue with working vacations and negative customers is introduced. The arrival processes of positive customers and negative customers are Poisson. Upon the arrival of a positive customer, if the server is busy the customer would enter an orbit of infinite size and the orbital customers send their requests for service with a constant retrial rate. The single server takes an exp...

This paper treats a discrete-time single-server finite-buffer exhaustive (singleand multiple-) vacation queueing system with discrete-time Markovian arrival process (D-MAP). The service and vacation times are generally distributed random variables and their durations are integral multiples of a slot duration. We obtain the queue-length distributions at departure, service completion, vacation te...