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Currently, the knowledge of queueing network is an important tool for modeling many complex communication systems. In this work, we consider a tandem open queueing network consisting of multiple Geo/Geo/1 clients, and a server with batch service queue. All of queues are finite-buffer discrete-time. The main purpose of this work is to analyze the average delay and the overflow probability of messages from each client through the system. To solve the problem, we firstly transform the model with plenty of clients and one server into one client and one server according to the coupling clients with independent arrivals. Next, we calculate the stationary distribution of queue lengths of all nodes by the knowledge of Bivariate Discrete Time Markov Chains. Then, we analyze the performance metrics of messages from each client through the queueing network. Finally, simulation results verify the effectiveness of the analytical method and draw some constructive conclusions.

This paper presents constructive solutions to stochastic cash balance problems. The model studied is in a periodic review framework with convex holding and shortage costs levied both in the beginning and at the end of each period. Transaction costs are linear, with the possibility of unequal fixed and proportional parts for orders and disposals. Optimal myopic solutions are presented for convex and linear costs. The application of an integral of the cumulative demand distribution yields simple formulae for solving the exact values of the policy parameters. The logistic distribution is used to obtain results readily applicable in day-to-day decision-making. Approximations of the Wilson formula type are developed and compared with earlier contributions. Conditions for the optimality of myopic policies are also presented. Stationary solutions are developed, and compared with myopic results in order to evaluate the amount of suboptimality. The stationary distribution and the optimal policy are given for the bilateral exponential demand distribution case. All results have been programmed and tested against the local finance market data.

The problem of the existence of a stationary distribution and the convergence towards it in a certain semistochastic model for the growth of a population is considered. It is assumed that the population grows according to a deterministic equation, but at certain times there are catastrophes, which lead to a decrease in the population level. The hazard function for the occurrence of catastrophes is a function of the population level only. The size of these jumps have a distribution that depends on the population size immediately before the catastrophe. A constructive method for finding the stationary distribution is given.