Myron Hlynka

An M/G/1 retrial queue with balking and retrials during service

We consider an M/G/1 retrial queue with general retrial times. Customers may balk or renege at particular times. The server is subject to breakdown (with repairs). While the server is being repaired, the customer in service can either remain in the service position or leave and return, while maintaining its rights to the server. We find a stability condition for this system. In the steady state, the joint distribution of the server state and queue length is obtained, leading to useful measures of the system, such as the probability of an empty system, the mean number of customers in the retrial queue and the expected retrial time.

Observing Queues Before Joining

We consider a queueing system with two servers, each with its own queue. The interarrival times are generally distributed. The service time for each server is exponentially distributed but the rates may be different. No jockeying between the two queues is allowed. We consider situations in which a smart customer can delay joining a queue until some arrivals or service departures have been observed. All other customers join the shortest queue. We find conditions under which the smart customer can lower its expected sojourn time in the system by waiting and observing rather than immediately joining the shortest queue.

Rapid on-site defibrillation versus community program.

INTRODUCTION For patients who suffer out-of-hospital cardiac arrest, the time from collapse to initial defibrillation is the single most important factor that affects survival to hospital discharge. The purpose of this study was to compare the survival rates of cardiac arrest victims within an institution that has a rapid defibrillation program with those of its own urban community, tiered EMS system. METHODS A logistic regression analysis of a retrospective data series (n = 23) and comparative analysis to a second retrospective data series (n = 724) were gathered for the study period September 1994 to September 1999. The first data series included all persons at Casino Windsor who suffered a cardiac arrest. Data collected included: age, gender, death/survival (neurologically intact discharge), presenting rhythm (ventricular fibrillation (VF), ventricular tachycardia (VT), or other), time of collapse, time to arrival of security personnel, time to initiation of cardiopulmonary resuscitation (CPR) prior to defibrillation (when applicable), time to arrival of staff nurse, time to initial defibrillation, and time to return of spontaneous circulation (if any). Significantly, all arrests within this series were witnessed by the surveillance camera systems, allowing time of collapse to be accurately determined rather than estimated. These data were compared to those of similar events, times, and intervals for all patients in the greater Windsor area who suffered cardiac arrest. This second series was based upon the Ontario Prehospital Advanced Life Support (OPALS) Study database, as coordinated by the Clinical Epidemiology Unit of the Ottawa Hospital, University of Ottawa. RESULTS The Casino Windsor had 23 cases of cardiac arrests. Of the cases, 13 (56.5%) were male and 10 (43.5%) were female. All cases (100%) were witnessed. The average of the ages was 61.1 years, of the time to initial defibrillation was 7.7 minutes, and of the time for EMS to reach the patient was 13.3 minutes. The presenting rhythm was VF/VT in 91% of the case. Fifteen patients were discharged alive from hospital for a 65% survival rate. The Greater Windsor Study area included 668 cases of out-of-hospital cardiac arrest: Of these, 410 (61.4%) were male and 258 (38.6%) were female, 365 (54.6%) were witnessed, and 303 (45.4%) were not witnessed. The initial rhythm was VF/VT was in 34.3%. Thirty-seven (5.5%) were discharged alive from the hospital. CONCLUSION This study provides further evidence that PAD Programs may enhance cardiac arrest survival rates and should be considered for any venue with large numbers of adults as well as areas with difficult medical access.

On the best case performance of hit and run methods for detecting necessary constraints

The hit and run methods are probabilistic algorithms that can be used to detect necessary (nonredundant) constraints in systems of linear constraints. These methods construct random sequences of lines that pass through the feasible region. These lines intersect the boundary of the region at twohit-points, each identifying a necessary constraint. In order to study the statistical performance of such methods it is assumed that the probabilities of hitting particular constraints are the same for every iteration. An indication of the best case performance of these methods can be determined by minimizing, with respect to the hit probabilities, the expected value of the number of iterations required to detect all necessary constraints. We give a set of isolated strong local minimizers and prove that for two, three and four necessary constraints the set of local minimizers is the complete set of global minimizers. We conjecture that this is also the case for any number of necessary constraints. The results in this paper also apply to sampling problems (e.g., balls from an urn) and to the coupon collectors problem.

The secretary problem for a random walk

The secretary problem for a random walk is described. A particle has equal probabilities of moving j steps up or j steps down. The optimal strategy of picking the maximum height in n steps without the opportunity of recall is found. The best strategy is shown to be exactly the same as the naive strategy of choosing the first element of the sequence. The theory is extended to symmetric continuous distributions.

Comments on duality of queues with finite buffer size

This paper introduces a new method for studying duality in queues. The concept of quasi-duality is defined and various properties are established, under the assumption of a finite buffer.

Trading nodal storage capacity with incremental transmission capacity in supra-high-speed packet-switching nets

The authors present queuing-theoretic formulations for trading nodal storage capacity (i.e., buffers) requirements for the incremental transmission capacity of the links in supra-high-speed packet-switching nets. The performance criterion used is the mean nodal forwarding time. The results are useful for designing all-optical packet-switching telecommunication networks where the designer must compute the amount of incremental transmission capacity needed to eliminate a prespecified number of nodal buffers while preserving the same mean (or average) nodal forwarding time. A single optical buffer can be easily implemented by using a simple optical delay line. An example is included using a very-high-speed regular digraph as an architecture of a macro-switching fabric.

Examples of Applications of Queueing Theory in Canada

Abstract As part of the 50th anniversary of the Canadian Operational Research Society, we reviewed queueing applications by Canadian researchers and practitioners. We concentrated on finding real applications, but also considered theoretical contributions to applied areas that have been developed by the authors based on real applications. There were a surprising number of applications, many not well documented. Thus, this paper features examples of queueing theory applications over a spectrum of areas, years and types. One conclusion is that some of the successful queueing applications were achieved and ameliorated by using simple principles gained from studying queues and not by complex mathematical models.

Job sequencing using an expert

Abstract We study the benefits of using an experts estimates of unknown service times to order a batch of jobs of fixed size prior to machine processing. Although the estimates may be incorrect, the jobs are reordered based on the estimates to reduce the sum of the flow times of all jobs in the batch. We examine a system with two job times and obtain closed analytical results for the expectation of total flow time. Furthermore, we analyze the amount by which the experts ordering is better than random processing order, and how the experts accuracy affects these results.

SC-TC trade-off in supra-high-speed packet switched networks

Queuing formulations for trading off nodal storage capacity (SC) with the incremental transmission capacity (TC) of links in supra-high-speed (>10/sup 8/ b/s) packet-switched communication networks are presented. The performance criterion used is the mean nodal forwarding time. The results are useful for designing all-optical packet-switching telecommunication networks where the designer needs to compute the amount of incremental TC (ITC) needed to eliminate a specified number of nodal buffers (SC) while preserving the mean nodal forwarding time.<<ETX>>