In this paper we consider a like-queue production system in which server startupand breakdowns are possible. The server is turned on (i.e. begins startup)when N units are accumulated in the system and off when the system is empty.We model this system by an M[x]/M/1 queue withserver breakdowns and startup time under the N policy. The arrival rate varies according to the server's status:off, startup, busy, or breakdown.While the server is working, he is subject tobreakdowns according to a Poisson process. When the server breaks down, he requires repairat a repair facility, where the repair time follows the negative exponential distribution.We study the steady-state behaviour of the system size distribution atstationary point of time as well as the queue size distribution at departure point of timeand obtain some useful results.The total expected cost function per unit time is developed to determine the optimal operatingpolicy at a minimum cost. This paper provides the minimum expected cost and the optimal operatingpolicy based on assumed numerical values of the system parameters. Sensitivity analysis is also provided.

We derive an ESTA property for marked point processes similar to Wolff's PASTA property for ordinary (non-marked) point processes, via a stochastic integral approach. This new ESTA property allows us to extend a known result on the conditional PASTA property and to derive an ASTA property for batch arrival processes. We also present an application of our results.

Existence and finiteness of the sample-mean limit of sojourn times of jobs in a queueing system are investigated. The queueing system operates under rather general multiprocessor disciplines allowing job classes and priorities. The input stream of jobs consisting of job classes and interarrival and processing times is stationary and ergodic and may contain batch arrivals. Existence of the sample-mean limit is proved by means of the superadditive ergodic theorem, and its finiteness is controlled by uniform mixing of the input stream.

Kulkarni (1986) derived expressions for the expected waiting times for customers of two types who arrive in batches at a single-channel repeated orders queueing system. We propose another method of solving this problem and extend Kulkarni&s result to the case of N≧2 classes of customers.

Expressions are derived for the expected waiting times for the customers of two types who arrive in batches (in a compound Poisson fashion) at a single-server queueing station with no waiting room. Those who cannot get served immediately keep returning to the system after random exponential amounts of time until they get served. The result is shown to agree with similar results for three special cases studied in the literature.

A single-server queue with batch arrivals in a non-homogeneous Poisson process and with balking is studied with respect to the busy period, using supplementary variables. A system of integral equations is obtained on the base of which the transforms are expressed in series. For the homogeneous case, assuming finite waiting room, the solutions are obtained via Cramer's rule. This gives asymptotic expressions for the expectations for large arrival intensity. An efficiency measure giving the long run loss probability is given. For a special case contour integral representations are given as solutions.