On the Heterogeneous M/G/n Blocking System in a Random Environment

This paper discusses the equilibrium behaviour of the generalized M/G/n blocking system with heterogeneous servers. The system is evolving in a random environment controlled by an irreducible, aperiodic, m-state Markov chain Z(t). This paper deals with the main characteristics, such as utilization, the average length of busy period of the system, the mean number of occupied servers and the probability of blocking. Finally, numerical examples illustrate the problem in question.     

Asymptotic Analysis of Finite-Source M/GI/1 Retrial Queueing Systems with Collisions and Server Subject to Breakdowns and Repairs

Methodology and Computing in Applied Probability - This paper deals with a retrial queuing system with a finite number of sources and collision of the customers, where the server is subject to...     

The effects of service disciplines on the performance of a nonreliable terminal system

In this paper, we consider a stochastic queueing model for the performance evaluaton of a real-life computer system consisting of n terminals connected with a CPU. A user at terminal i has thinking and processing time depending on the index i. Let us suppose that the operational system is subject to random breakdowns, which may be software or hardware ones, stopping the service both at the terminals and at the CPU. The failure-free operation times of the system and the restoration times are random variables. Busy terminals are also subject to random breakdowns not affecting the system operation. The failure-free operation times and the repair times of a busy terminal i are random variables with distribution function depending on index i. The breakdowns are serviced by a single repairman providing preemptive priority to the system's failure, while the restoration at the terminals are carried out according to the FIFO rule. We assume that each user generates only one job at a time, and he waits at the CPU before he starts thinking again, that is, the terminal is inactive while waiting at the CPU, and it cannot break down. All random variables involved in the model construction are assumed to be exponentially distributed and independent of each other. The aim of this paper is to investigate the effect of different service disciplines, such as FIFO, processor sharing, priority processor sharing, and polling, on the main performance measures, such as utilizations, response times, throughput, and mean queue length. Supported by the Hungarian National Foundation for Scientific Research (grant No. ORKA T014974/95). Proceedings of the Seminar on Stability Problems for Stochastic Models, Hajdúszoboszló. Hungary, 1997, Part II.     

On the finite-source G/M/r queue

The aim of the present paper is to give the main characteristics of the finite-source $\text{G}\text{/}\text{M}\text{/r}$ queue in equilibrium. Here unit i stays in the source for a random time having general distribution function F_i(x) with density f_i(x). The service times of all units are assumed to be identically and exponentially distributed random variables with means 1/μ. It is shown that the solution to this $\text{G}\text{/}\text{M}\text{/r}$ model is similar in most important respects to that for the M/M/r model.     

Reliability analysis of complex communication systems

This paper deals with a first-come, first-served (FCFS) queueing model to analyze the asymptotic behavior of a heterogeneous finite-source communication system with a single processor. Each source and the processor are assumed to operate in independent random environments, allowing the arrival and service processes to be Markov-modulated ones. Each message is characterized by its own exponentially distributed source and processing time with parameter, depending on the state of the corresponding environment, that is, the arrival and service rates are subject to random fluctuations. Assuming that the arrival rates of the messages are many times greater than their service rates (“fast” arrival), it is shown that the time to the first system failure converges in distribution, under appropriate norming, to an exponentially distributed random variable. Some simple examples are considered to illustrate the effectiveness of the method proposed by comparing the approximate results to the exact ones. Supported by the Hungarian National Foundation for Scientific Research (grant No. OTKA T14974/95). Proceedings of the Seminar on Stability Problems for Stochastic Models, Vologda, Russia, 1998, Part II.     

A queueing model for a nonreliable multiterminal system with polling scheduling

This paper deals with a nonhomogeneous finite-source queueing model to describe the performance of a multiterminal system subject to random breakdowns under the polling service discipline. The model studied here is a closed queueing network which has three service stations. a CPU (single server), terminals (infinite server), a repairman (single server), and a finite number of customers (jobs) that have distinct service rates at the service stations. The CPU's repair has preemptive priority over the terminal repairs, and failure of the CPU stops the service of the other stations, thus the nodes are not independent. It can be viewed as a continuation of papers by the authors (see references), which discussed a FIFO (first-in, first-out) and a PPS (priority processor sharing) serviced queueing model subject to random breakdowns. All random variables are assumed to be independent and exponentially distributed. The system behavior can be described by a Markov chain, but the number of states is very large. The purpose of this paper is to give a recursive computational approach to solve steady-state equations and to illustrate the problem in question using some numerical results. Supported by the Hungarian National Foundation for Scientific Research (grant Nos. OTKA T014974/95 and T016933/95) Proceedings of the Seminar on Stability Problems for Stochastic Models. Hajdúszoboszló, Hungary, 1997, Part, II.