Adjoining Batch Markov Arrival Processes of a Markov Chain

A batch Markov arrival process（BMAP） X^＊=（N, J） is a 2-dimensional Markov process with two components, one is the counting process N and the other one is the phase process J. It is proved that the phase process is a time-homogeneous Markov chain with a finite state-space, or for short, Markov chain. In this paper,a new and inverse problem is proposed firstly： given a Markov chain J, can we deploy a process N such that the 2-dimensional process X^＊=（N, J） is a BMAP？ The process X^＊=（N, J） is said to be an adjoining BMAP for the Markov chain J. For a given Markov chain the adjoining processes exist and they are not unique. Two kinds of adjoining BMAPs have been constructed. One is the BMAPs with fixed constant batches, the other one is the BMAPs with independent and identically distributed（i.i.d） random batches. The method we used in this paper is not the usual matrix-analytic method of studying BMAP, it is a path-analytic method. We constructed directly sample paths of adjoining BMAPs. The expressions of characteristic（D_k, k = 0, 1, 2· · ·）and transition probabilities of the adjoining BMAP are obtained by the density matrix Q of the given Markov chain J. Moreover, we obtained two frontal Theorems. We present these expressions in the first time.

Computational analysis of(MAP_1,MAP_2)/(PH_1,PH_2)/N queues with finite buffer in wireless cellular networks

This paper studies a queueing model with the finite buffer of capacity K in wireless cellular networks, which has two types of arriving calls--handoff and originating calls, both of which follow the Markov arriving process with different rates. The channel holding times of the two types of calls follow different phase-type distributions. Firstly, the joint distribution of two queue lengths is derived, and then the dropping and blocking probabilities, the mean queue length and the mean waiting time from the joint distribution are gotten. Finally, numerical examples show the impact of different call arrival rates on the performance measures.

Performance of the(BMAP_1, BMAP_2 )/(PH_1, PH_2 )/N Retrial Queueing System with Finite Buffer

This paper consider the （BMAP1, BMAP2）/（PH1, PH2）/N retrial queue with finite-position buffer. The behavior of the system is described in terms of continuous time multi-dimensional Markov chain. Arriving type I calls find all servers busy and join the buffer, if the positions of the buffer are insufficient, they can go to orbit. Arriving type II calls find all servers busy and join the orbit directly. Each server can provide two types heterogeneous services with Phase-type （PH） time distribution to every arriving call （including types I and II calls）, arriving calls have an option to choose either type of services. The model is quite general enough to cover most of the systems in communication networks. We derive the ergodicity condition, the stationary distribution and the main performance characteristics of the system. The effects of various parameters on the system performance measures are illustrated numerically.