This paper analyzes renewal input state dependent queue with $N$- policy wherein the server takes exactly one vacation. Using the supplementary variable technique and recursive method, we derive the steady state system length distributions at various epochs. Various performance measures has been presented. Finally, some numerical  computations in the form of graphs are presented to show the par...

This investigation deals with MX/G/1 queueing model with setup, bulk- arrival, loss-delay and balking. The provision of second optional service apart from essential service by an unreliable server is taken into consideration. We assume that the delay customers join the queue when server is busy whereas loss customers depart from the system. After receiving the essential service, the customers m...

This paper compares two discrete-time single-server queueing models with queues. In both models, the server is available to a queue probability 1/2 at each service opportunity. Since obtaining easy-to-evaluate expressions for joint moments not feasible, we rely on heavy-traffic limit approach. The correlation coefficient of queue-contents computed via solution two-dimensional functional equatio...

We propose to use a mathematical method based on stochastic comparisons of Markov chains in order to derive performance indice bounds‎. ‎The main goal of this paper is to investigate various monotonicity properties of a single server retrial queue with first-come-first-served (FCFS) orbit and general retrial times using the stochastic ordering techniques‎.

This paper represents linkage network of queues consisting of biserial and parallel servers linked to a common server in series with a flowshop scheduling system consisting of two machines. The significant transportation time of the jobs from one machine to another is also considered. Further, the completion time of jobs/customers (waiting time + service time) in the queue network is the set...

— We consider in this paper the steady state behaviour of a Queueing System with queue length dependent additional server facility wherein arrivais occur in batches of variable size. Whenever the queue length in front of the first server reaches a certain lenght, the system adds another server. Steady state probabilities and expected queue lengths in Single Server System and Additional Server S...

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, 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...