This paper studies two stochastic batch Markovian arrival and batch Markovian service single server queue BMAP/BMSP/1 queue Models (A) and (B) with randomly varying k* distinct environments. The arrival process of the queue has matrix representation {Dm i : 0 ≤ m ≤ M} of order ki describing the BMAP and the service process has matrix representation {Sn i : 0 ≤ n ≤ N} of order k′i describing the...

Batch-arrival queueing models can be used in 1) many practical situations, such as the analysis of message packetization in data communication systems. In general it is difficult, if not impossible, to find tractable expressions for the waiting-time probabilities of individual customers. It is, therefore, useful to have easily computable approximations for these probabilities. This paper gives ...

This paper analyzes a single-server finite-buffer vacation (single and multiple) queue wherein the input process follows a discrete-time batch Markovian arrival process (D-BMAP). The service and vacation times are generally distributed and their durations are integral multiples of a slot duration. We obtain the state probabilities at service completion, vacation termination, arbitrary, and prea...

In this paper, we show how to utilize the expectation-maximization (EM) algorithm for efficient and numerical stable parameter estimation of the batch Markovian arrival process (BMAP). In fact, effective computational formulas for the E-step of the EM algorithm are presented, which utilize the well-known randomization technique and a stable calculation of Poisson jump probabilities. Moreover, w...

We consider an MXI ell queueing system with N-policy and single vacation. As soon as the system becomes empty, the server leaves the system for a vacation of random length 11: When he returns from the vacation, if the system size is greater than or equal to a pretermined value N(threshold), he begins to serve the customers. If not, the server waits in the system until the system size reaches or...

Abstract. Queueing systems with batch service have been investigated extensively during the past decades. However, nearly all the studied models share the common feature that an uncorrelated arrival process is considered, which is unrealistic in several real-life situations. In this paper, we study a discrete-time queueing model, with a server that only initiates service when the amount of cust...

We consider herein a single-server queueing system with finite buffer and batch Markovian arrival process. Customers staying in the may have lower or higher priority. Immediately after each of customer is assigned lowest priority timer set for it, which defined as random variable distributed according to phase law having two absorbing states. After enters one states, leave forever (get lost) ch...