A Light Traffic Approximation for a Single-Server Queue

1984 ◽  
Vol 9 (4) ◽  
pp. 624-628 ◽  
Author(s):  
D. J. Daley ◽  
T. Rolski
Keyword(s):  
Single Server ◽  
Single Server Queue ◽  
Light Traffic ◽  
Server Queue

On queues in discrete regenerative environments, with application to the second of two queues in series

1979 ◽  
Vol 11 (04) ◽  
pp. 851-869 ◽  
Author(s):  
K. Balagopal
Keyword(s):  
Limit Theorems ◽  
Heavy Traffic ◽  
Single Server ◽  
Single Server Queue ◽  
Light Traffic ◽  
Queuing Model ◽  
Heavy Traffic Limit ◽  
Server Queue ◽  
In Series ◽  
Queues In Series

Let Un be the time between the nth and (n + 1)th arrivals to a single-server queuing system, and Vn the nth arrival's service time. There are quite a few models in which {Un, Vn , n ≥ 1} is a regenerative sequence. In this paper, some light and heavy traffic limit theorems are proved solely under this assumption; some of the light traffic results, and all the heavy traffic results, are new for two such models treated earlier by the author; and all the results are new for the semi-Markov queuing model. In the last three sections, the results are applied to a single-server queue whose input is the output of a G/G/1 queue functioning in light traffic.

On queues in discrete regenerative environments, with application to the second of two queues in series

1979 ◽  
Vol 11 (4) ◽  
pp. 851-869 ◽  
Author(s):  
K. Balagopal
Keyword(s):  
Limit Theorems ◽  
Heavy Traffic ◽  
Single Server ◽  
Single Server Queue ◽  
Light Traffic ◽  
Queuing Model ◽  
Heavy Traffic Limit ◽  
Server Queue ◽  
In Series ◽  
Queues In Series

Let Un be the time between the nth and (n + 1)th arrivals to a single-server queuing system, and Vn the nth arrival's service time. There are quite a few models in which {Un, Vn, n ≥ 1} is a regenerative sequence. In this paper, some light and heavy traffic limit theorems are proved solely under this assumption; some of the light traffic results, and all the heavy traffic results, are new for two such models treated earlier by the author; and all the results are new for the semi-Markov queuing model.In the last three sections, the results are applied to a single-server queue whose input is the output of a G/G/1 queue functioning in light traffic.

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.

Loss Probability of a Burst Arrival Finite Queue with Synchronized Service

1992 ◽  
Vol 6 (2) ◽  
pp. 201-216 ◽  
Author(s):  
Masakiyo Miyazawa
Keyword(s):  
Markov Chain ◽  
Loss Probability ◽  
Buffer Size ◽  
Embedded Markov Chain ◽  
Main Concern ◽  
Single Server ◽  
Finite Buffer ◽  
Single Server Queue ◽  
Server Queue ◽  
Computation Algorithm

We are concerned with a burst arrival single-server queue, where arrivals of cells in a burst are synchronized with a constant service time. The main concern is with the loss probability of cells for the queue with a finite buffer. We analyze an embedded Markov chain at departure instants of cells and get a kind of lumpability for its state space. Based on these results, this paper proposes a computation algorithm for its stationary distribution and the loss probability. Closed formulas are obtained for the first two moments of the numbers of cells and active bursts when the buffer size is infinite.

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