scholarly journals A result in queueing theory

1978 ◽  
Vol 19 (1) ◽  
pp. 125-129
Author(s):  
A. Ghosal
Keyword(s):  
Waiting Time ◽  
Queueing Theory ◽  
Waiting Times ◽  
Queueing Systems ◽  
Random Variable ◽  
Equilibrium Distribution Function ◽  
Single Server ◽  
Queue Discipline ◽  
The Difference ◽  
Practical Implications

In a single-server queueing system, subject to the queue discipline ‘First come first served’, the equilibrium distribution function of the waiting time of a server depends on the distribution of the random variable (u) which is the difference between the service time and the inter-arrival time. If in two queueing systems u's are equivalent in distribution, the waiting times are also equivalent in distribution (known result). It has been shown in this note that equivalence in waiting time distributions does not necessarily imply equivalence in distributions of u's. The proof is heuristic. This result has useful practical implications.

The total waiting time in a busy period of a stable single-server queue, I.

1969 ◽  
Vol 6 (03) ◽  
pp. 550-564 ◽  
Author(s):  
D. J. Daley
Keyword(s):  
Waiting Time ◽  
Queueing Theory ◽  
Busy Period ◽  
Queueing System ◽  
Road Traffic ◽  
Waiting Times ◽  
Random Variable ◽  
Single Server ◽  
Single Server Queue ◽  
Server Queue

A quantity of particular interest in the study of (road) traffic jams is the total waiting time X of all vehicles involved in a given hold-up (Gaver (1969): see note following (2.3) below and the first paragraph of Section 5). With certain assumptions on the process this random variable X is the same as the sum of waiting times of customers in a busy period of a GI/G/1 queueing system, and it is the object of this paper and its sequel to study the random variable in the queueing theory context.

The total waiting time in a busy period of a stable single-server queue, I.

1969 ◽  
Vol 6 (3) ◽  
pp. 550-564 ◽  
Author(s):  
D. J. Daley
Keyword(s):  
Waiting Time ◽  
Queueing Theory ◽  
Busy Period ◽  
Queueing System ◽  
Road Traffic ◽  
Waiting Times ◽  
Random Variable ◽  
Single Server ◽  
Single Server Queue ◽  
Server Queue

A quantity of particular interest in the study of (road) traffic jams is the total waiting time X of all vehicles involved in a given hold-up (Gaver (1969): see note following (2.3) below and the first paragraph of Section 5). With certain assumptions on the process this random variable X is the same as the sum of waiting times of customers in a busy period of a GI/G/1 queueing system, and it is the object of this paper and its sequel to study the random variable in the queueing theory context.

A family of delay-dependent dynamic priority queueing systems

1984 ◽  
Vol 16 (1) ◽  
pp. 9-9
Author(s):  
P. K. Reeser
Keyword(s):  
Waiting Times ◽  
Queueing Systems ◽  
Priority Queue ◽  
Single Server ◽  
State Behavior ◽  
Dynamic Priority ◽  
Queue Discipline ◽  
Delay Dependent ◽  
First Time ◽  
Priority Queueing

We consider a family of single-server queueing systems with two priority classes. The system operates under a dynamic priority queue discipline in which the relative priorities of customers increase with their waiting times, and which can be characterized by the urgency number. We investigate the transient as well as the steady-state behavior of the virtual waiting times of the two classes of customer as functions of the urgency number. Stochastic orderings, the joint distribution, and surprising limit results for these processes are obtained for the first time.

HOW TO REPORT AND MONITOR THE PERFORMANCE OF WAITING LIST MANAGEMENT

2002 ◽  
Vol 18 (3) ◽  
pp. 611-618
Author(s):  
Markus Torkki ◽  
Miika Linna ◽  
Seppo Seitsalo ◽  
Pekka Paavolainen
Keyword(s):  
Hallux Valgus ◽  
Waiting Time ◽  
Varicose Vein ◽  
Elective Surgery ◽  
Waiting Times ◽  
Waiting List ◽  
Mean Waiting Time ◽  
Number Of Patients ◽  
Potential Problems ◽  
Queue Discipline

Objectives: Potential problems concerning waiting list management are often monitored using mean waiting times based on empirical samples. However, the appropriateness of mean waiting time as an indicator of access can be questioned if a waiting list is not managed well, e.g., if the queue discipline is violated. This study was performed to find out about the queue discipline in waiting lists for elective surgery to reveal potential discrepancies in waiting list management. Methods: There were 1,774 waiting list patients for hallux valgus or varicose vein surgery or sterilization. The waiting time distributions of patients receiving surgery and of patients still waiting for an operation are presented in column charts. The charts are compared with two model charts. One model chart presents a high queue discipline (first in—first out) and another a poor queue discipline (random) queue. Results: There were significant differences in waiting list management across hospitals and patient categories. Examples of a poor queue discipline were found in queues for hallux valgus and varicose vein operations. Conclusions: A routine waiting list reporting should be used to guarantee the quality of waiting list management and to pinpoint potential problems in access. It is important to monitor not only the number of patients in the waiting list but also the queue discipline and the balance between demand and supply of surgical services. The purpose for this type of reporting is to ensure that the priority setting made at health policy level also works in practise.

On a tandem queueing model with identical service times at both counters, II

1979 ◽  
Vol 11 (3) ◽  
pp. 644-659 ◽  
Author(s):  
O. J. Boxma
Keyword(s):  
Heavy Traffic ◽  
Queueing Systems ◽  
Single Server ◽  
Service Time Distribution ◽  
In Series ◽  
Mean And Variance ◽  
Queues In Series ◽  
The Mean ◽  
Service Times ◽  
Practical Implications

This paper is devoted to the practical implications of the theoretical results obtained in Part I [1] for queueing systems consisting of two single-server queues in series in which the service times of an arbitrary customer at both queues are identical. For this purpose some tables and graphs are included. A comparison is made—mainly by numerical and asymptotic techniques—between the following two phenomena: (i) the queueing behaviour at the second counter of the two-stage tandem queue and (ii) the queueing behaviour at a single-server queue with the same offered (Poisson) traffic as the first counter and the same service-time distribution as the second counter. This comparison makes it possible to assess the influence of the first counter on the queueing behaviour at the second counter. In particular we note that placing the first counter in front of the second counter in heavy traffic significantly reduces both the mean and variance of the total time spent in the second system.

On a property of a refusals stream

1997 ◽  
Vol 34 (03) ◽  
pp. 800-805 ◽  
Author(s):  
Vyacheslav M. Abramov
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Busy Period ◽  
Elementary Proof ◽  
Queueing System ◽  
Queueing Systems ◽  
Single Server ◽  
Wide Family

This paper consists of two parts. The first part provides a more elementary proof of the asymptotic theorem of the refusals stream for an M/GI/1/n queueing system discussed in Abramov (1991a). The central property of the refusals stream discussed in the second part of this paper is that, if the expectations of interarrival and service time of an M/GI/1/n queueing system are equal to each other, then the expectation of the number of refusals during a busy period is equal to 1. This property is extended for a wide family of single-server queueing systems with refusals including, for example, queueing systems with bounded waiting time.

Convex ordering of the attained waiting times in single-server queues and related problems

1991 ◽  
Vol 28 (02) ◽  
pp. 433-445 ◽  
Author(s):  
Masakiyo Miyazawa ◽  
Genji Yamazaki
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Waiting Times ◽  
Service Discipline ◽  
Single Server ◽  
Waiting Time Distribution ◽  
Convex Order ◽  
Convex Ordering ◽  
Single Server Queues ◽  
Service Disciplines

The attained waiting time of customers in service of the G/G/1 queue is compared for various work-conserving service disciplines. It is proved that the attained waiting time distribution is minimized (maximized) in convex order when the discipline is FCFS (PR-LCFS). We apply the result to characterize finiteness of moments of the attained waiting time in the GI/GI/1 queue with an arbitrary work-conserving service discipline. In this discussion, some interesting relationships are obtained for a PR-LCFS queue.

scholarly journals The Multiphase Queuing System of the Rijeka Airport

Pomorstvo ◽  
2019 ◽  
Vol 33 (2) ◽  
pp. 205-209
Author(s):  
Svjetlana Hess ◽  
Ana Grbčić
Keyword(s):  
Performance Indicators ◽  
Queueing Theory ◽  
Rare Case ◽  
Queueing System ◽  
Service System ◽  
Waiting Times ◽  
Real Problem ◽  
Single Server ◽  
Scientific Contribution ◽  
The Real

The paper gives an overview of the real system as a multiphase single server queuing problem, which is a rare case in papers dealing with the application of the queueing theory. The methodological and scientific contribution of this paper is primarily in setting up the model of the real problem applying the multiphase queueing theory. The research of service system at Rijeka Airport may allow the airport to be more competitive by increasing service quality. The existing performance measures have been evaluated in order to improve Rijeka Airport queueing system, as a record number of passengers is to be expected in the next few years. Performance indicators have pointed out how the system handles congestion. The research is also focused on defining potential bottlenecks and comparing the results with IATA guidelines in terms of maximum waiting times.

Waiting times for patterns in a sequence of multistate trials

2001 ◽  
Vol 38 (2) ◽  
pp. 508-518 ◽  
Author(s):  
Demetrios L. Antzoulakos
Keyword(s):  
Markov Chain ◽  
Waiting Time ◽  
Waiting Times ◽  
Random Variable ◽  
Finite Markov Chain ◽  
Finite Markov Chain Imbedding ◽  
Markov Chain Imbedding ◽  
Markov Chain Imbedding Method ◽  
Runs And Patterns ◽  
Imbedding Method

Let Xn, n ≥ 1 be a sequence of trials taking values in a given set A, let ∊ be a pattern (simple or compound), and let Xr,∊ be a random variable denoting the waiting time for the rth occurrence of ∊. In the present article a finite Markov chain imbedding method is developed for the study of Xr,∊ in the case of the non-overlapping and overlapping way of counting runs and patterns. Several extensions and generalizations are also discussed.

A solvable model for a finite-capacity queueing system

1985 ◽  
Vol 22 (4) ◽  
pp. 903-911 ◽  
Author(s):  
V. Giorno ◽  
C. Negri ◽  
A. G. Nobile
Keyword(s):  
Queueing System ◽  
Waiting Times ◽  
Queueing Systems ◽  
Solvable Model ◽  
Probability Density Functions ◽  
Single Server ◽  
Finite Capacity ◽  
System Service ◽  
Transient Probabilities ◽  
Number Of Customers

Single–server–single-queue–FIFO-discipline queueing systems are considered in which at most a finite number of customers N can be present in the system. Service and arrival rates are taken to be dependent upon that state of the system. Interarrival intervals, service intervals, waiting times and busy periods are studied, and the results obtained are used to investigate the features of a special queueing model characterized by parameters (λ (Ν –n), μn). This model retains the qualitative features of the C-model proposed by Conolly [2] and Chan and Conolly [1]. However, quite unlike the latter, it also leads to closed-form expressions for the transient probabilities, the interarrival and service probability density functions and their moments, as well as the effective interarrival and service densities and their moments. Finally, some computational results are given to compare the model discussed in this paper with the C-model.

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