Since an M D queue is represented by a Markov chain we can consider the set of all the M D queues as a subset of Markov chains A geometric structures is induced from the geometric structure of the set of Markov chains which forms an exponential family In this paper we show that in the large deviation of the tail probability of the queue length of an M D the rate function and a twisted Markov ch...

We consider a discrete-time single-server queue with arrivals governed by a stationary Markov chain, where no arrivals are assumed to occur only when the Markov chain is in a particular state. This assumption implies that o -periods in the arrival process are i.i.d. and geometrically distributed. For this queue, we establish the exact relationship between queue length distributions in a nite-bu...

In this paper, we discuss the waiting-time distribution for a finite-space, single-server queueing system, in which customers arrive singly following Poisson process and server operates under (a,b)-bulk service rule. The system has finite-buffer capacity ‘N’ excluding batch service. service-time of batches follows general distribution, is independent arrival process. We first develop an alterna...

[Tip: Study the MC, QT, and Little's law lectures together: CTMC (MC lecture), M/M/1 queue (QT lecture), Little's law lecture (when deriving the mean response time from mean number of customers), DTMC (MC lecture), M/M/1 queue derivation using DTMC analysis, derive distribution of response time in M/M/1 queue (QT lecture), relation between Markov property and mem-oryless property (MC lecture), ...

Hierarchical Cellular Networks provide an enhanced use of the indoor networks. These two lower layers called picocell and femtocell consist both high and low speed users. To prevent the dropping and blocking probabilities of ongoing calls in a network, cells are spitted into the small sizes. Although, many effective approaches are used but these delaying calls reach in a queue until a channel b...

A novel approach for obtaining the response time in a discrete time tandem queue with blocking, using matrix analytic methods, is presented. The approach sets up the appropriate Markov chain based on the age of the leading customer in the first queue, together with other auxiliary variables. By this approach the response time is obtained with only minor additional effort after obtaining the sta...

Two-tier cellular networks provide an enhanced use of the networks' resources for both high and low speed users. However, they cause an increase in the number of handoffs between cells due to having smaller cell sizes in the microcell tier. An effective approach used to prevent the dropping of ongoing calls in a network is delaying these calls in a queue until a channel becomes available. In th...