scholarly journals Asymptotical analysis of a non-Markovian queueing system with renewal input process and random capacity of customers

2017 ◽  
pp. 30-38
Author(s):  
Ekaterina Yu. Lisovskaya ◽  
◽  
Svetlana P. Moiseeva
Keyword(s):  
Queueing System ◽  
Input Process ◽  
Random Capacity ◽  
Asymptotical Analysis

scholarly journals A queueing system with moving average input process and batch arrivals

1965 ◽  
Vol 5 (4) ◽  
pp. 434-442 ◽  
Author(s):  
C. Pearce
Keyword(s):  
Queueing System ◽  
Moving Average ◽  
Limiting Distribution ◽  
Input Process ◽  
Batch Arrivals

In a recent paper by P. D. Finch and myself [1], the solution for the limiting distribution of a moving average queueing system was obtained. In this paper the system is generalised to the case of batch arrivals in batches of size ρ > 1.

Analysis of a Discrete-Time Queueing System with a Markov-Modulated input Process and constant service Rate

1996 ◽  
Vol 10 (3) ◽  
pp. 429-441 ◽  
Author(s):  
Woo-Yong Choi ◽  
Chi-Hyuck Jun
Keyword(s):  
Discrete Time ◽  
Queueing System ◽  
Service Rate ◽  
System State ◽  
Input Process ◽  
New Approach ◽  
One Dimensional ◽  
Markov Modulated ◽  
Modulated Process ◽  
Renewal Cycle

We propose a new approach to the analysis of a discrete-time queueing system whose input is generated by a Markov-modulated process and whose service rate is constant. Renewal cycles are identified and the system state on each renewal cycle is modeled as a one-dimensional Markov chain.

Single-server queues with impatient customers

1984 ◽  
Vol 16 (4) ◽  
pp. 887-905 ◽  
Author(s):  
F. Baccelli ◽  
P. Boyer ◽  
G. Hebuterne
Keyword(s):  
Waiting Time ◽  
Queueing System ◽  
Distribution Functions ◽  
Single Server ◽  
Waiting Time Distribution ◽  
Input Process ◽  
Poisson Input ◽  
Virtual Waiting Time ◽  
Random Threshold ◽  
The Stability

We consider a single-server queueing system in which a customer gives up whenever his waiting time is larger than a random threshold, his patience time. In the case of a GI/GI/1 queue with i.i.d. patience times, we establish the extensions of the classical GI/GI/1 formulae concerning the stability condition and the relation between actual and virtual waiting-time distribution functions. We also prove that these last two distribution functions coincide in the case of a Poisson input process and determine their common law.

scholarly journals The single server queueing system with Non-recurrent input-process and Erlang service time

1963 ◽  
Vol 3 (2) ◽  
pp. 220-236 ◽  
Author(s):  
P. D. Finch
Keyword(s):  
Service Time ◽  
Queueing System ◽  
Single Server ◽  
Input Process ◽  
Service Times ◽  
Image Position

We consider a single server queueing system in which customers arrive at the instants t0, t1, …, tm, …. We write τm = tm+1 − tm, m ≧ 0. There is a single server with distribution of service times B(x) given by where k is an integer not less than unity.

On the M/G/1 queue by additional inputs

1984 ◽  
Vol 21 (1) ◽  
pp. 129-142 ◽  
Author(s):  
Teunis J. Ott
Keyword(s):  
Busy Period ◽  
Queueing System ◽  
Arrival Process ◽  
Single Server ◽  
Input Process ◽  
Stochastic Monotonicity ◽  
General Process ◽  
Virtual Waiting Time ◽  
Waiting Time Process ◽  
Monotonicity Results

A single-server queueing system is studied, the input into which consists of the sum of two independent stochastic processes. One of these is an ‘M/G' type input process, the other a much more general process which need not be Markov. There are two types of busy period, depending on which arrival process started the busy period. Stochastic monotonicity results are derived and it is found that under a stationarity-like condition the probability of being in a busy period which started with an ‘M/G' arrival is independent of time and is the same it would be with the ‘M/G' process as only input process. Also, distributional results are obtained for the virtual waiting-time process, and these results are used to reduce the study of a single-server queueing system with as input the sum of independent ‘M/G' and ‘GI/G' input streams to the study of a related GI/G/1 queueing system.The purpose of this paper is to pave the way for a study of an M/G/1 queueing system with periodic arrivals of additional work, and for optimal scheduling of maintenance processes in certain real-time computer systems.

scholarly journals A second look at a queueing system with moving average input process

1965 ◽  
Vol 5 (1) ◽  
pp. 100-106 ◽  
Author(s):  
P. D. Finch ◽  
C. Pearce
Keyword(s):  
Queueing System ◽  
Moving Average ◽  
Time Interval ◽  
Single Server ◽  
Input Process ◽  
Second Look ◽  
Queue Discipline ◽  
Image Position

We consider a single-server queueing system with first-come first-served queue discipline in which (i) customers arrive at the instants 0 = A0 < A1 < A2 < …, with time interval between the mth and (m+1)th arrivals

On the M/G/1 queue by additional inputs

1984 ◽  
Vol 21 (01) ◽  
pp. 129-142
Author(s):  
Teunis J. Ott
Keyword(s):  
Busy Period ◽  
Queueing System ◽  
Arrival Process ◽  
Single Server ◽  
Input Process ◽  
Stochastic Monotonicity ◽  
General Process ◽  
Virtual Waiting Time ◽  
Waiting Time Process ◽  
Monotonicity Results

A single-server queueing system is studied, the input into which consists of the sum of two independent stochastic processes. One of these is an ‘M/G' type input process, the other a much more general process which need not be Markov. There are two types of busy period, depending on which arrival process started the busy period. Stochastic monotonicity results are derived and it is found that under a stationarity-like condition the probability of being in a busy period which started with an ‘M/G' arrival is independent of time and is the same it would be with the ‘M/G' process as only input process. Also, distributional results are obtained for the virtual waiting-time process, and these results are used to reduce the study of a single-server queueing system with as input the sum of independent ‘M/G' and ‘GI/G' input streams to the study of a related GI/G/1 queueing system. The purpose of this paper is to pave the way for a study of an M/G/1 queueing system with periodic arrivals of additional work, and for optimal scheduling of maintenance processes in certain real-time computer systems.

Single-server queues with impatient customers

1984 ◽  
Vol 16 (04) ◽  
pp. 887-905 ◽  
Author(s):  
F. Baccelli ◽  
P. Boyer ◽  
G. Hebuterne
Keyword(s):  
Waiting Time ◽  
Queueing System ◽  
Distribution Functions ◽  
Single Server ◽  
Waiting Time Distribution ◽  
Input Process ◽  
Poisson Input ◽  
Virtual Waiting Time ◽  
Random Threshold ◽  
The Stability

We consider a single-server queueing system in which a customer gives up whenever his waiting time is larger than a random threshold, his patience time. In the case of a GI/GI/1 queue with i.i.d. patience times, we establish the extensions of the classical GI/GI/1 formulae concerning the stability condition and the relation between actual and virtual waiting-time distribution functions. We also prove that these last two distribution functions coincide in the case of a Poisson input process and determine their common law.

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