Estimating warranty costs during the life cycle of a product is important to the manufacturer, who has to plan for creating a fund for warranty reserves. Replacement or repair costs associated with product-failure within the warranty period are drawn from this fund. This paper considers a policy where warranty is not renewed on product failure within the warranty period but the product is minimally repaired by the manufacturer. This implies that, on repair, the failure rate of the item remains the same as just prior to failure. Repair costs are assumed to depend on the product age. Such policies are suitable for complex and expensive products where repair typically involves a small part of the product. s-Expected warranty costs and amount of warranty reserves, based on a selected level of s-confidence, are derived. Applications of the results to various product market situations are considered. The results demonstrate how cost information can be used to decide and determine the warranty length.

We consider a traffic model where a single source generates traffic having J (J/spl ges/2) quality of service (QoS) classes, QoS in this case described by a cell loss probability objective /spl epsiv//sub j/ for QoS class j. We assume that /spl epsiv//sub 1//spl ges//spl epsiv//sub 2//spl ges/.../spl ges//spl epsiv//sub J/, in other words, class J has the most stringent QoS requirements and class 1 the least. The traffic from K such independent heterogeneous Markov-modulated fluid sources is multiplexed into a single buffer of size B. There are J-1 thresholds.>

This paper is concerned with the optimal flow control of an ATM switching element in a broadband-integrated services digital network. We model the switching element as a stochastic fluid-flow system with a finite buffer, a constant output rate, and Markov-modulated fluid input. There is a cost of holding fluid and a reward for admitting the fluid to the buffer. We study the optimal flow control policies that minimize the fetal expected discounted cost. We analyze the problem by two different approaches and show that the optimal policy is of the turnpike type with the turnpike levels dependent on the states of the Markov-modulated source. We also state sufficient conditions under which the optimal turnpike levels are monotonic functions of the states of the Markov-modulated source.>

Traffic consisting of two classes (0 and 1) arrives at a buffer in a bursty fashion. The type-0 traffic is always admitted into the buffer (of size B/sub 0/) as long as there is space for it. Type-1 traffic is admitted to the buffer only if the buffer content does not exceed a threshold B/sub 1spl les/B/sub 0/. The authors develop an analytical model to determine the bandwidth allocation in order to ensure that the packet loss probability of type-i traffic does not exceed /spl epsisub i/, where 0>

Abstract In this work, we compute the distribution of L*, the length of a shortest (s, t) path, in a directed network G with a source node s and a sink node t and whose arc lengths are independent, nonnegative, integer valued random variables having finite support. We construct a discrete time Markov chain with a single absorbing state and associate costs with each transition such that the total cost incurred by this chain until absorption has the same distribution as does L*. We show that the transition probability matrix of this chain has an upper triangular structure and exploit this property to develop numerically stable algorithms for computing the distribution of L* and its moments. All the algorithms are recursive in nature and are illustrated by several examples. © 1993 by John Wiley & Sons, Inc.

Abstract An exact cut in a source‐sink network is a set of arcs which interesects each source‐sink path in exactly one arc. This paper investigates the problem of finding a maximum weight exact cut in a network. The problem is shown to be polynomially equivalent to that of determining the relevant arcs (arcs on at least one source‐sink path) in the network and is NP‐hard for general directed networks. There are, however, several important classes of network—including undirected networks—for which polynominal time algorithms do exist to solve the maximum weight exact cut problem.

In this paper we consider the queueing analysis of a fault-tolerant computer system. The failure/repair behavior of the server is modeled by an irreducible continuous-time Markov chain. Jobs arrive in a Poisson fashion to the system and are serviced according to FCFS discipline. A failure may cause the loss of the work already done on the job in service, if any; in this case the interrupted job is repeated as soon as the server is ready to deliver service. In addition to the delays due to failures and repairs, jobs suffer delays due to queueing. We present an exact queueing analysig of the system and study the steady-state behavior of the number of jobs in the system. As a numerical example, we consider a system with two processors subject to failures and repairs.

Queueing models provide a useful tool for predicting the performance of many service systems including computer systems, telecommunication systems, computer/communication networks and flexible manufacturing systems. Traditional queueing models predict system performance under the assumption that all service facilities provide failure-free service. It must, however, be acknowledged that service facilities do experience failures and that they get repaired. In recent years, it has been increasingly recognized that this separation of performance and reliability/availability models is no longer adequate.

Abstract This paper develops methods for the exact computation of the distribution of the length of the shortest path from a given source node s to a given sink node t in a directed network in which the arc lengths are independent and exponentially distributed random variables. A continuous time Markov chain with a single absorbing state is constructed from the original network such that the time until absorption into this absorbing state starting from the initial state is equal to the length of the shortest path in the original network. It is shown that the state space of this Markov chain is the set of all minimal (s, t) cuts in the network and that its generator matrix is upper triangular. Algorithms are described for computing the distribution and moments of the length of the shortest path based on this Markov chain representation. Algorithms are also developed for computing the probability that a given (s, t) path is the shortest path in the network and for computing the conditional distribution of the length of a path given that it is the shortest (s, t) path in the network. All algorithms are numerically stable and are illustrated by several numerical examples.