A Markov queueing system having heterogeneous servers under a long-run average criterion is analyzed. A direct proof of the optimality of a stationary, Markov policy is given using martingale methods. Simultaneously, the problem is reduced to a linear programming problem. Analysis of the LP for a system having finite queueing length shows the optimal policy is not always of threshold type.

It has recently been shown that, for the FCFS G/G/1 queue, the workload and attained waiting time of a customer in service have the same stationary distribution. We show that, for a general queueing system setting, the workload and total attained waiting time of customers in service are identical in average but the equality of the distributions is not true in general except for the FCFS G/G/1 queue.

In Giorno et al. (1988) a new method for constructing first-passage-time probability density functions is outlined. This rests on the possibility of constructing the transition p.d.f. of a new time-homogeneous diffusion process in terms of a preassigned transition p.d.f. without making use of the classical space-time transformations of the Kolmogorov equation (Ricciardi (1976)).

In the present paper we give an extension of this result to the case of a diffusion process X(t) which is not necessarily time-homogeneous, and a few examples are presented.

In this paper we find new bounds for the reliability of coherent systems of independent components with increasing failure rate average (IFRA) lifetimes. These bounds are based on certain bounds available for the survival functions of IFRA random variables and the fact that the IFRA class of life distributions is closed under the formation of coherent systems. These bounds are compared with other applicable bounds in this case. An illustration of explicit computations of the bounds is provided for the bridge structure with components having independent gamma life distributions.

We study single-server queueing models where in addition to regular arriving customers, there are negative arrivals. A negative arrival has the effect of removing a customer from the queue. The way in which this removal is specified gives rise to several different models. Unlike the standard FIFO GI/GI/1 model, the stability conditions for these new models may depend upon more than just the arrival and service rates; the entire distributions of interarrival and service times may be involved.

Let T be a non-empty subset of η X n stochastic matrices. Define The sequence T1, T2, · ·· is called a Markov set-chain. An important problem in this area is to determine when such a set-chain converges. This paper gives a notion of a sequential limiting set and shows how it can be used to obtain a result on set-chain convergence.

Change of measure up to fixed times or stopping times is the theme of the famous Cameron–Martin–Girsanov formula. The paper studies change of measure up to random times which are not stopping times of the natural filtration. The ultimate aim is to build up a family of interesting models for physics and chemistry.

Consider an i.i.d. sequence of non-negative random variables (X1, · ··, Xn) with known distribution F. Consider decision rules for selecting a maximum number of the subject to the following constraints: (1) the sum of the elements selected must not exceed a given constant c > 0, and (2) the must be inspected in strict sequence with the decision to accept or reject an element being final at the time it is inspected. Coffman et al. (1987) proved that there exists such a rule that maximizes the expected number En(c) of variables selected, and determined the asymptotics of En(c) for special distributions. Here we determine the asymptotics of En(cn) for very general choices of sequences (cn) and of F, by showing that En(c) is very close to an easily computable number. Our proofs are (somewhat deceptively) very simple, and rely on an appropriate stopping-time argument.

In the excavation of archaeological remains of high value, a search tool with low cost can be used at first, but if we reach a stratum which is very likely to contain valuable material we must use a search tool with high efficiency to reduce the risk of destruction of the remains even if this is more expensive. Which tool should we use at each time? Furthermore, if the search costs too much in comparison with the reward of detection, it is not profitable to go on searching for ever. When should we stop the search? We answer these questions for continuous and discrete models.

It is shown that, in a superposition of finitely many independent renewal processes, an observation from the limiting (when t →∞) joint distribution of backward and forward recurrence times at t can be simulated by simulating an observation of the pair (UW, (1 – U)W), where U and Ware independent random variables with U ~ uniform(0, 1) and W distributed according to the limiting total life distribution of the superposition process.

A counterexample is given to demonstrate that a previously proposed characterization of optimal inspection policy for series systems is not correct in the discounted case. A set of valid necessary conditions is provided which leads to the characterization of optimality for a special case. The limiting case of these necessary conditions is also examined.