A queueing system with impatient customers

1985 ◽  
Vol 22 (03) ◽  
pp. 688-696 ◽  
Author(s):  
A. G. De Kok ◽  
H. C. Tijms
Keyword(s):  
Performance Measures ◽  
Queueing System ◽  
Fixed Time ◽  
Single Server ◽  
Impatient Customers ◽  
Average Delay ◽  
Practical Applications ◽  
Poisson Input ◽  
General Service Times ◽  
General Service

A queueing situation often encountered in practice is that in which customers wait for service for a limited time only and leave the system if not served during that time. This paper considers a single-server queueing system with Poisson input and general service times, where a customer becomes a lost customer when his service has not begun within a fixed time after his arrival. For performance measures like the fraction of customers who are lost and the average delay in queue of a customer we obtain exact and approximate results that are useful for practical applications.

A queueing system with impatient customers

1985 ◽  
Vol 22 (3) ◽  
pp. 688-696 ◽  
Author(s):  
A. G. De Kok ◽  
H. C. Tijms
Keyword(s):  
Performance Measures ◽  
Queueing System ◽  
Fixed Time ◽  
Single Server ◽  
Impatient Customers ◽  
Average Delay ◽  
Practical Applications ◽  
Poisson Input ◽  
General Service Times ◽  
General Service

A queueing situation often encountered in practice is that in which customers wait for service for a limited time only and leave the system if not served during that time. This paper considers a single-server queueing system with Poisson input and general service times, where a customer becomes a lost customer when his service has not begun within a fixed time after his arrival. For performance measures like the fraction of customers who are lost and the average delay in queue of a customer we obtain exact and approximate results that are useful for practical applications.

A single-server queue with limited virtual waiting time

1974 ◽  
Vol 11 (03) ◽  
pp. 612-617 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Waiting Time ◽  
Single Server ◽  
Single Server Queue ◽  
Limiting Distributions ◽  
Poisson Input ◽  
Virtual Waiting Time ◽  
General Service Times ◽  
Server Queue ◽  
Service Times ◽  
General Service

The limiting distributions of the actual waiting time and the virtual waiting time are determined for a single-server queue with Poisson input and general service times in the case where there are two types of services and no customer can stay in the system longer than an interval of length m.

A single-server queue with limited virtual waiting time

1974 ◽  
Vol 11 (3) ◽  
pp. 612-617 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Waiting Time ◽  
Single Server ◽  
Single Server Queue ◽  
Limiting Distributions ◽  
Poisson Input ◽  
Virtual Waiting Time ◽  
General Service Times ◽  
Server Queue ◽  
Service Times ◽  
General Service

The limiting distributions of the actual waiting time and the virtual waiting time are determined for a single-server queue with Poisson input and general service times in the case where there are two types of services and no customer can stay in the system longer than an interval of length m.

Some perturbation results for the single-server queue with Poisson input

1965 ◽  
Vol 2 (2) ◽  
pp. 462-466 ◽  
Author(s):  
A. M. Hasofer
Keyword(s):  
Service Time ◽  
Single Server ◽  
Single Server Queue ◽  
Poisson Input ◽  
Server Queue ◽  
Image Position ◽  
General Service

In a previous paper [2] the author has studied the single-server queue with non-homogeneous Poisson input and general service time, with particular emphasis on the case when the parameter of the Poisson input is of the form

scholarly journals A Priority Queue with Many Customer Types, Correlated Arrivals and Changing Priorities

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1292
Author(s):  
Seokjun Lee ◽  
Sergei Dudin ◽  
Olga Dudina ◽  
Chesoong Kim ◽  
Valentina Klimenok
Keyword(s):  
Markov Chain ◽  
Waiting Time ◽  
Performance Indicators ◽  
Queueing System ◽  
Priority Queue ◽  
First Aid ◽  
Single Server ◽  
Finite Buffer ◽  
Impatient Customers ◽  
Arrival Times

A single-server queueing system with a finite buffer, several types of impatient customers, and non-preemptive priorities is analyzed. The initial priority of a customer can increase during its waiting time in the queue. The behavior of the system is described by a multi-dimensional Markov chain. The generator of this chain, having essential dependencies between the components, is derived and formulas for computation of the most important performance indicators of the system are presented. The dependence of some of these indicators on the capacity of the buffer space is illustrated. The profound effect of the phenomenon of correlation of successive inter-arrival times and variance of the service time is numerically demonstrated. Results can be used for the optimization of dispatching various types of customers in information transmission systems, emergency departments and first aid stations, perishable foods supply chains, etc.

On queues with periodic Poisson input

1981 ◽  
Vol 18 (04) ◽  
pp. 889-900 ◽  
Author(s):  
Austin J. Lemoine
Keyword(s):  
Waiting Time ◽  
Direct Proof ◽  
Poisson Model ◽  
Fixed Time ◽  
Time Of Day ◽  
Asymptotic Distributions ◽  
Single Server ◽  
Service Time Distribution ◽  
Asymptotic Results ◽  
Poisson Input

This paper is concerned with asymptotic results for a single-server queue having periodic Poisson input and general service-time distribution, and carries forward the analysis of this model initiated in Harrison and Lemoine. First, it is shown that a theorem of Hooke relating the stationary virtual and actual waiting-time distributions for the GI/G/1 queue extends to the periodic Poisson model; it is then pointed out that Hooke's theorem leads to the extension (developed in [3]) of a related theorem of Takács. Second, it is demonstrated that the asymptotic distribution for the server-load process at a fixed ‘time of day' coincides with the distribution for the supremum, over the time horizon [0,∞), of the sum of a stationary compound Poisson process with negative drift and a continuous periodic function. Some implications of this characterization result for the computation and approximation of the asymptotic distributions are then discussed, including a direct proof, for the periodic Poisson case, of a recent result of Rolski comparing mean asymptotic customer waiting time with that of a corresponding M/G/1 system.

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