Achieving prescribed mean waiting times in a single-server queueing system

1991 ◽  
Vol 27 (6) ◽  
pp. 878-882
Author(s):  
E. A. Timofeev
Keyword(s):  
Queueing System ◽  
Waiting Times ◽  
Single Server

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.

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.

The suprema of the actual and virtual waiting times during a busy cycle of the K m/K n/1 queueing system

1972 ◽  
Vol 4 (02) ◽  
pp. 339-356
Author(s):  
J. W. Cohen
Keyword(s):  
Limit Theorems ◽  
Queueing System ◽  
Waiting Times ◽  
Analytic Description ◽  
Single Server ◽  
Arrival Times ◽  
Asymptotic Expressions ◽  
Virtual Waiting Time ◽  
Stieltjes Transforms ◽  
Busy Cycle

For the single server queueing system, whose distributions of service and inter-arrival times have rational Laplace-Stieltjes transforms, limit theorems are derived for the supremum of the virtual waiting time during k successive busy cycles for k→∞. Similarly, for the supremum of the actual waiting times of all customers arriving in k successive busy cycles. Only the cases with the load of the system less than one and equal to one are considered. The limit distributions are extreme value distributions. The results are obtained by first deriving a number of asymptotic expressions for the quantities which govern the analytic description of the system K m /K n /1. Using these asymptotic relations limit theorems for entrance times can also be obtained, a few examples are given.

A solvable model for a finite-capacity queueing system

1985 ◽  
Vol 22 (04) ◽  
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.

The suprema of the actual and virtual waiting times during a busy cycle of the Km/Kn/1 queueing system

1972 ◽  
Vol 4 (2) ◽  
pp. 339-356 ◽  
Author(s):  
J. W. Cohen
Keyword(s):  
Limit Theorems ◽  
Queueing System ◽  
Waiting Times ◽  
Analytic Description ◽  
Single Server ◽  
Arrival Times ◽  
Asymptotic Expressions ◽  
Virtual Waiting Time ◽  
Stieltjes Transforms ◽  
Busy Cycle

For the single server queueing system, whose distributions of service and inter-arrival times have rational Laplace-Stieltjes transforms, limit theorems are derived for the supremum of the virtual waiting time during k successive busy cycles for k→∞. Similarly, for the supremum of the actual waiting times of all customers arriving in k successive busy cycles. Only the cases with the load of the system less than one and equal to one are considered. The limit distributions are extreme value distributions. The results are obtained by first deriving a number of asymptotic expressions for the quantities which govern the analytic description of the system Km/Kn/1. Using these asymptotic relations limit theorems for entrance times can also be obtained, a few examples are given.

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.

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

1979 ◽  
Vol 11 (3) ◽  
pp. 616-643 ◽  
Author(s):  
O. J. Boxma
Keyword(s):  
Waiting Times ◽  
Sufficient Conditions ◽  
Complete Analysis ◽  
Single Server ◽  
Stationary Distributions ◽  
In Series ◽  
Queues In Series ◽  
Service Times ◽  
Necessary And Sufficient ◽  
Insight Into

This paper considers a queueing system consisting of two single-server queues in series, in which the service times of an arbitrary customer at both queues are identical. Customers arrive at the first queue according to a Poisson process.Of this model, which is of importance in modern network design, a rather complete analysis will be given. The results include necessary and sufficient conditions for stationarity of the tandem system, expressions for the joint stationary distributions of the actual waiting times at both queues and of the virtual waiting times at both queues, and explicit expressions (i.e., not in transform form) for the stationary distributions of the sojourn times and of the actual and virtual waiting times at the second queue.In Part II (pp. 644–659) these results will be used to obtain asymptotic and numerical results, which will provide more insight into the general phenomenon of tandem queueing with correlated service times at the consecutive queues.

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