In this letter, we derive the CDF (cumulative distribution function) of k th contact distance (CD) and nearest neighbor (NND) xmlns:xlink="http://www.w3.org/1999/xlink"> n -dimensional ( xmlns:xlink="http://www.w3.org/1999/xlink">n -D) Matérn cluster process (MCP). We present a new approach ...

This paper analyzes a discrete-time batch arrival queue with working vacations. In a GeoX/G/1 system, the server works at a lower speed during the vacation period which becomes a lower speed operation period. This model is more appropriate for the communication systemswith the transmit units arrived in batches.We formulate the system as an embeddedMarkov chain at the departure epoch and by theM...

Abstract: This paper treats a discrete-time batch arrival queue with geometrically working vacations and vacation interruption. The main purpose of this paper is to present a performance analysis of this system. For this purpose, we first derive the probability generating function (PGF) of the stationary system length at the departure epochs based on the embedded Markov chain technique. Next, w...

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...

For queueing models that can be analyzed as (embedded) Markov chains, many results are presented in terms of the probability generating function (PGF) of the stationary queue length distribution. Queueing models that belong to this category are bulk service queues, M/G/l and G/M/l-type queues, and discrete or discrete-time queues. The determination of the PGF typically requires a fixed number o...

In this paper we present an exact steady-state analysis of a discrete-time Geo/G/1 queueing system with working vacations, where the server can keep on working, but at a slower speed during the vacation period. The transition probability matrix describing this queuing model can be seen as an M/G/1-type matrix form. This allows us to derive the probability generating function (PGF) of the statio...

For queueing models that can be analyzed as (embedded) Markov chains, many results are presented in terms of the probability generating function (PGF) of the stationary queue length distribution. Queueing models that belong to this category are bulk service queues, M/G/l and G/M/l-type queues, and discrete or discrete-time queues. The determination of the PGF typically requires a fixed number o...

For queueing models that can be analyzed as (embedded) Markov chains, many results are presented in terms of the probability generating function (PGF) of the stationary queue length distribution. Queueing models that belong to this category are bulk service queues, M/G/l and G/M/l-type queues, and discrete or discrete-time queues. The determination of the PGF typically requires a fixed number o...

In this paper we study a Geo/T-IPH/1 queue model, where T-IPH denotes the discrete time phase type distribution defined on a birth-and-death process with countably many states. The queue model can be described by a quasi-birth-anddeath (QBD) process with countably phases. Using the operator-geometric solution method, we first give the expression of the operator and the joint stationary distribu...

In this paper we consider the analysis of M/G/1 queue with working vacation. In contrast to the previous literature where the working vacation starts when all customers are served (exhaustive discipline) we consider the case where the vacation period starts when the customers present at the system at beginning of the service period are served (gated discipline). The analysis of the model with g...