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.

Hierarchical modeling of stochastic manufacturing and service systems

This paper presents a review of methodologies for analyzing stochastic manufacturing and service systems. On the basis of the scale and level of details of operations, we can study stochastic systems using micro-,meso-, and macro-scopic models. Such a classification unifies stochastic modeling theory. For each model type,we highlight the advantages and disadvantages and the applicable situations. Micro-scopic models are based on quasi-birth-and-death process because of the phase-type distributed service times and/or Markov arrival processes.Such models are appropriate for modeling the detailed operations of a manufacturing system with relatively small number of servers(production facilities). By contrast,meso-scopic and macro-scopic models are based on the functional central limit theorem(FCLT) and functional strong law of large numbers(FSLLN), respectively, under heavy-traffic regimes. These high-level models are appropriate for modeling large-scale service systems with many servers, such as call centers or large service networks. This review will help practitioners select the appropriate level of modeling to enhance their understanding of the dynamic behavior of manufacturing or service systems. Enhanced understanding will ensure that optimal policies can be designed to improve system performance. Researchers in operation analytics and optimization of manufacturing and logistics also benefit from such a review.

Cold standby repairable system with working vacations and vacation interruption

This paper studies a cold standby repairable system with working vacations and vacation interruption. The repairman's multiple vacations policy, the working vacations policy and the vacation interruption are considered simultaneously. The lifetime of components follows a phase-type(PH) distribution. The repair time in the regular repair period and the working vacation period follow other two PH distributions at different rates. For this system, the vector-valued Markov process governing the system is constructed. We obtain several important performance measures for the system in transient and stationary regimes applying matrixanalytic methods. Finally, a numerical example is given to illustrate the results obtained.