The effect of correlated exponential service times on single server tandem queues

An investigation via simulation of system performance of two stage queues in series (single server, first-come, first-served) under the assumption of correlated exponential service times indicates that the system's behavior is quite sensitive to departures from the traditional assumption of mutually independent service times, especially at higher utilizations. That service times at the various stages of a tandem queueing system for a given customer should be correlated is intuitively appealing and apparently not at all atypical. Since tandem queues occur frequently, e.g. production lines and the logistics therewith associated, it is incumbent on both the practitioner and the theoretician that they be aware of the marked effects that may be induced by correlated service times. For the case of infinite interstage storage, system performance is improved by positive correlation and impaired by negative correlation. This change in system performance is reversed however for zero interstage storage and depends on the value of the utilization rate for the case where interstage storage equals unity. The effect due to correlation is shown to be statistically significant using spectral analytic techniques. For correlation equal unity and infinite interstage storage, results are provided for two through twenty-five stages in series to suggest how adding stages affects system performance for ρ>0. In this extreme case of correlation, adding stages has an effect on system performance which depends markedly on the utilization rate. Recursive formulae for the waiting time per customer for the cases of zero, one, and infinite interstage storage are derived.     

Probabilistic priorities in the M/G/1 queue

A simple method is presented for deriving the mean and variance of the queueing time distribution in an M/G/1 queue when the priorities assigned to customers have an assignment probability distribution. Several examples illustrate the results. The mean and variance of the queueing time distribution for the longest service time discipline are derived, and its disadvantages are discussed.     

A primal simplex algorithm to solve a rectilinear distance facility location problem

This paper considers the problem of locating m new facilities in the plane so as to minimize a weighted rectangular distance between the new facilities and n existing facilities. A special purpose primal simplex algorithm is developed to solve this problem. The algorithm will maintain at all times a basis of dimension m by m; however, because of the triangularity of the basis matrix, it will not be necessary to form a basis inverse explicitly.     

Sequencing independent jobs with a single resource

This paper examines problems of sequencing n jobs for processing by a single resource to minimize a function of job completion times, when the availability of the resource varies over time. A number of well-known results for single-machine problems which can be applied with little or no modification to the corresponding variable-resource problems are given. However, it is shown that the problem of minimizing the weighted sum of completion times provides an exception.     

Storage problems when demand is “all or nothing”

An inventory of physical goods or storage space (in a communications system buffer, for instance) often experiences “all or nothing” demand: if a demand of random size D can be immediately and entirely filled from stock it is satisfied, but otherwise it vanishes. Probabilistic properties of the resulting inventory level are discussed analytically, both for the single buffer and for multiple buffer problems. Numerical results are presented.     

The United States Coast Guard Computer-Assisted Search Planning system (CASP)

This paper provides an overview of the Computer-Assisted Search Planning (CASP) system developed for the United States Coast Guard. The CASP information processing methodology is based upon Monte Carlo simulation to obtain an initial probability distribution for target location and to update this distribution to account for drift due to currents and winds. A multiple scenario approach is employed to generate the initial probability distribution. Bayesian updating is used to reflect negative information obtained from unsuccessful search. The principal output of the CASP system is a sequence of probability “maps” which display the current target location probability distributions throughout the time period of interest. CASP also provides guidance for allocating search effort based upon optimal search theory.     

Spike swapping in basis reinversion

During basis reinversion of either a product form or elimination form linear programming system, it may become necessary to swap spike columns to effect the reinversion and maintain the desired sparsity characteristics. This note shows that the only spikes which need be examined when an interchange is required are those not yet processed in the current external bump.     

Techniques for establishing ergodic and recurrence properties of continuous-valued markov chains

We present techniques for classifying Markov chains with a continuous state space as either ergodic or recurrent. These methods are analogous to those of Foster for countable space chains. The theory is presented in the first half of the paper, while the second half consists of examples illustrating these techniques. The technique for proving ergodicity involves, in practice, three steps: showing that the chain is irreducible in a suitable sense; verifying that the mean hitting times on certain (usually bounded) sets are bounded, by using a “mean drift” criterion analogous to that of Foster; and finally, checking that the chain is such that bounded mean hitting times for these sets does actually imply ergodicity. The examples comprise a number of known and new results: using our techniques we investigate random walks, queues with waiting-time-dependent service times, dams with general and random-release rules, the s-S inventory model, and feedback models.