This paper presents a transient solution for the system size in an M/M/2 queue where the service rates of the servers are not identical with the possibility of catastrophes at the system. The time dependent probabilities for the number in the system are obtained. The steady state probabilities of the system size are also provided. Some important performance measures are derived.

We derive an integral equation for the transient probabilities and expected number in the queue for the multiserver queue with Poisson arrivals, exponential service for timevarying arrival and departure rates, and a time-varying number of servers. The method is a straightforward application of generating functions. We can express pĉ−1(t), the probability that ĉ − 1 customers are in the queue or...

It is pointed out that the moments of phase-space particle density at freeze-out can be determined from the coincidence probabilities of the events observed in multiparticle production. A method to measure the coincidence probabilities is described and its validity examined. Recently we have proposed [1] a method for measuring the average of the particle density in multiparticle phase space. Ge...

A condition based preventive and corrective maintenance policy is proposed for a continuously operating system. The condition of the system is assumed to deteriorate with time. The model incorporates both deterioration as well as random common cause failures. The deterioration stages are modeled as discrete state processes. The system is put to random inspection to know the condition. The mean ...

By considering the master equation of the partially asymmetric diffusion process on a one-dimensional lattice, the most general boundary condition (i.e. interactions) for the multi-species reaction-diffusion processes is considered. Resulting system has various interactions including diffusion to left and right, two-particle interactions AαAβ → AγAδ and the extended n-particle drop-push interac...

We consider a bilateral birth-death process having sigmoidal-type rates. A thorough discussion on its transient behaviour is given, which includes studying symmetry properties of the transition probabilities, finding conditions leading to their bimodality, determining mean and variance of the process, and analyzing absorption problems in the presence of 1 or 2 boundaries. In particular, thanks ...

Continued Fractions method has been used to obtain a transient solution for the system size probabilities in an M/M/1 queue with instantaneous Bernoulli feedback subject to Catastrophes, Server Failures and Repairs. The steady state analysis of system size probabilities and some performance measures of the system are deduced. Further, Busy Period, Reliability and Availability of the model are a...