The Rate Conservation Law (RCL) of Miyazawa [18] is generalized to what we call a General Rate Conservation Law (GRCL) to cover processes of unbounded variation such as Brownian motion and more general Levy processes. The general setup is that of a time-stationary semimartingale Y = [Yt: t ≥ 0], which is allowed to have jumps. From an elementary application of Ito's formula together with the Palm inversion formula, we obtain a law that includes Miya-zawa's RCL as a special case. A variety of applications and connections with the RCL are given. For example, we show that using the GRCL, one can immediately obtain the noted steady-state decomposition results for vacation queueing models, including those obtained by Kella and Whitt [13] for Jump-Levy processes. Other examples include state-dependent diffusion processes such as the Ornstein-Uhlenbeck process.

This paper deals with two related approximations that were recently proposed for the loss probability in finite-buffer queues. The purpose of the paper is twofold: first, to provide better insight and more theoretical support for both approximations, and second, to show by an experimental study how well both approximations perform. An interesting empirical finding is that in many cases of practical interest the two approximations provide upper and lower bounds on the exact value of the loss probability.

We consider a single-server retrial queueing system where retrial time is inversely proportional to the number of customers in the system. A necessary and sufficient condition for the stability of the system is found. We obtain the Laplace transform of virtual waiting time and busy period. The transient distribution of the number of customers in the system is also obtained.

We consider a Markov decision chain with countable state space, finite action sets, and nonnegative costs. Conditions for the average cost optimality inequality to be an equality are derived. This extends work of Cavazos-Cadena [8]. It is shown that an optimal stationary policy must satisfy the optimality equation at all positive recurrent states. Structural results on the chain induced by an optimal stationary policy are derived. The results are employed in two examples to prove that any optimal stationary policy must be of critical number form.

A Markov decision chain with denumerable state space incurs two types of costs — for example, an operating cost and a holding cost. The objective is to minimize the expected average operating cost, subject to a constraint on the expected average holding cost. We prove the existence of an optimal constrained randomized stationary policy, for which the two stationary policies differ on at most one state. The examples treated are a packet communication system with reject option and a single-server queue with service rate control.

Two types of tasks are to be scheduled on a single processor under incomplete information about the task lengths. We derive the structure of optimal scheduling rules w.r.t. flowtime, as well as asymptotic approximations for a large number of tasks, when the length distributions belong to a one-parameter exponential family.

The minimum expected number of binomial group tests is lower bounded by the cost of a particular Huffman coding problem whose solution is known. Thus, the information lower bound in binomial group testing is improved when the probability that each item is defective is small.

The density of the first passage time in a nonstationary Gaussian process with random mean function can be approximated with arbitrary accuracy from a regression-type expansion. CROSSREG is a package of FORTRAN subroutines that perform intelligent transformations and numerical integrations to produce high-accuracy approximations with a minimum of computer time. The basic routines, collected in the unit ONEREG, give the density of the crossing time of a general bound. An additional set of routines make up the unit TWOREG, which also gives the bivariate density of the crossing time and the value of an accompanying process at the time of the crossing. These routines can be used to find the wavelength and amplitude density in any stationary Gaussian process. ONEREG and TWOREG are special cases of a routine MREG, which is the main routine in CROSSREG.