Machine Repair Model Research Articles

Delay models for contention trees in closed populations

In this paper we consider some models for contention resolution in cable networks, in case the contention pertains to requests from a finite population of stations and is carried out by means of contention trees. More specifically, we study a number of variants of the standard machine repair model, that differ in the service order at the repair facility. Considered service orders are first come first served, random order of service, and gated random order of service. For these variants, we study the sojourn time at the repair facility. In the case of the free access protocol for contention trees, the first two moments of the access delay in contention are accurately represented by those of the sojourn time at the repair facility under random order of service. In the case of the blocked access protocol, gated random order of service is shown to be more appropriate.

Transient solution of Markov models by combining adaptive and standard uniformization

Adaptive uniformization (AU) has been proposed to compute transient measures in continuous-time Markov chains and is especially attractive for solving large and stiff dependability models. The major advantage of AU is that it requires at most as many iterations as standard uniformization (SU), and often far fewer, thus resulting in substantial computation savings. However, this computation gain can be offset by the need to compute more complex jump-probabilities in AU, whose computation is more expensive than computing Poisson probabilities in SU. In particular, AU is computationally superior to SU if and only if the considered time instant is less than some threshold time value. To overcome this drawback, AU and SU are combined (AU/SU) so that AU is used early in the time interval, and SU is used over the rest of the time interval. AU/SU can be implemented so that: (1) the combination introduces only minor computation overhead, (2) the number of iterations required is almost as low as for AU, and (3) the cost of computing the jump probabilities is about as low as for SU. AU/SU yields a strict lower bound of the true result, within any desired pre-specified accuracy. The error bounds include the error introduced when the Fox/Glynn algorithm is used for computing Poisson probabilities; this algorithm is enhanced to optimize its error-bound characteristics. To demonstrate the benefits of AU/SU it is applied to a machine-repair model, using a version of combined AU/SU implemented in UltraSAN, a performance and dependability evaluation software package.

A comparison of allocation policies in a two-echelon repairable-item inventory model

The objective of this paper is to evaluate three allocation policies in a two-echelon machine repair model with state-dependent failure and repair rates. The first echelon consists of a number of bases that are served by a central depot in the second echelon. The operations at each base are modeled as a machine repair problem. Due to the complexity of the general model, a simulation study was conducted whereby the regenerative method of data collection was used. Two static and one dynamic allocation policy were compared with respect to five criteria. Based on the distribution of the observations, stochastic dominance tests were conducted and it was observed that static policies did not differ. The dynamic policy was found to be superior in a majority of the criteria.

Operations Research: Applications and Algorithms

Operations Research: Applications and Algorithms

Operations Research: Applications and Algorithms

Operations Research: Applications and Algorithms