Five different classical bulk queueing models with variations are considered from chapter II to chapter VI. This chapter and chapter VIII are devoted for the analysis of two different retrial queueing models. Retrial queueing system is characterized by the feature that the arriving customers, who encounter the server busy, join a virtual pool called orbit. An arbitrary customer in the orbit gen...

We consider an M/G/1 retrial queue, where the service time distribution has a regularly varying tail with index −β, 1 < β < 2. It is shown that the waiting time distribution has a regularly varying tail with index 1− β, and the pre-factor is determined explicitly. The result is obtained by comparing the waiting time in the M/G/1 retrial queue with the waiting time in the ordinary M/G/1 queue wi...

There are many practical situations that have both features of customer retrials and server vacations. The vacation policy is characterized by the vacation startup rules and vacation termination rules. The queueing system with retrials and vacations has been described in variety of ways according to the vacation rules and retrial policies such as constant retrial policy and linear retrial polic...

ABSTRACT We analyze a single server queue with modified Bernoulli server vacations based on exhaustive service. Unlike other vacation policies, we assume that only at the completion of service of the last customer in the system, the server has the option to take a vacation or to remain idle in the system waiting for the next customer to arrive. The service times of the customers have been assum...

Abstract Here a two-state batch arrivals and batch service Markovian queue with server vacation model has been taken into consideration for its mathematical modelling and performance analysis under transient state. The present Markovian queueing model considers a single server with multiple vacations and both arrivals and services in batches of variable size. Arriving customers are processed by...

Consider a single server retrial queueing system with pre-emptive priority service and single working vacation in which two types of customers arrive in a Poisson process with arrival rates ?1 for low and ?2 for high priority customers. We assume that regular service times follow an exponential distribution with parameters μ1 and μ2 correspondingly. The retrial is introduced for low priority cu...

Consider a single server retrial queueing system with preemptive priority service and single working vacation in which two types of customers arrive in a Poisson process with arrival rates λ1 for low and λ2 for high priority customers. We assume that regular service times follow an exponential distribution with parameters μ1 and μ2 correspondingly. The retrial is introduced for low priority cus...

Abstract: We analyze a discrete-time single-server queueing system whose arrival stream is a Bernoulli process and service times are generally distributed. An extension of the N -policy is considered: the server remains idle till the queue length becomes 1 i ≥ with probability i θ . After the idle (vacation) period, the server needs a random amount of startup time before serving. Moreover, afte...

This investigation deals with single server queueing system wherein the arrival of the units follow Poisson process with varying arrival rates in different states and the service time of the units is arbitrary (general) distributed. The server may take a vacation of a fixed duration or may continue to be available in the system for next service. Using the probability argument, we construct the ...

This paper presents a discrete-time single-server finite buffer N threshold policy queue with renewal input and discrete Markovian service process. The server terminates service whenever the system becomes empty, and recommences service as soon as the number of waiting customers in the queue is N . We obtain the system-length distributions at prearrival and arbitrary epochs using the supplement...