Simulation and Queueing Theory Applied to a Single-server Queue with Advertising and Balking

1993 ◽  
Vol 44 (4) ◽  
pp. 407-414 ◽  
Author(s):  
A van Ackere ◽  
P Ninios
Keyword(s):  
Queueing Theory ◽  
Single Server ◽  
Single Server Queue ◽  
Server Queue

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.

The single-server queue with service depending on queue size and with the preemptive-resume last-come–first-served queue discipline

1987 ◽  
Vol 24 (03) ◽  
pp. 758-767
Author(s):  
D. Fakinos
Keyword(s):  
Queueing System ◽  
Limiting Distribution ◽  
Single Server ◽  
Queue Size ◽  
Single Server Queue ◽  
Preemptive Resume ◽  
Server Queue ◽  
Queue Discipline ◽  
Service Times

This paper studies theGI/G/1 queueing system assuming that customers have service times depending on the queue size and also that they are served in accordance with the preemptive-resume last-come–first-served queue discipline. Expressions are given for the limiting distribution of the queue size and the remaining durations of the corresponding services, when the system is considered at arrival epochs, at departure epochs and continuously in time. Also these results are applied to some particular cases of the above queueing system.

scholarly journals New Approach for Finding Basic Performance Measures of Single Server Queue

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Siew Khew Koh ◽  
Ah Hin Pooi ◽  
Yi Fei Tan
Keyword(s):  
Stationary State ◽  
Queue Length ◽  
Length Distribution ◽  
Cumulative Distribution ◽  
System Capacity ◽  
Interarrival Time ◽  
Single Server ◽  
Single Server Queue ◽  
Queue Length Distribution ◽  
Server Queue

Consider the single server queue in which the system capacity is infinite and the customers are served on a first come, first served basis. Suppose the probability density functionf(t)and the cumulative distribution functionF(t)of the interarrival time are such that the ratef(t)/1-F(t)tends to a constant ast→∞, and the rate computed from the distribution of the service time tends to another constant. When the queue is in a stationary state, we derive a set of equations for the probabilities of the queue length and the states of the arrival and service processes. Solving the equations, we obtain approximate results for the stationary probabilities which can be used to obtain the stationary queue length distribution and waiting time distribution of a customer who arrives when the queue is in the stationary state.

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