On the virtual waiting time in an M/G/1 retrial queue

1991 ◽  
Vol 28 (2) ◽  
pp. 446-460 ◽  
Author(s):  
G. Falin ◽  
C. Fricker
Keyword(s):  
Waiting Time ◽  
Arrival Time ◽  
Retrial Queue ◽  
Single Server ◽  
Random Delay ◽  
Single Server Queue ◽  
Virtual Waiting Time ◽  
Server Queue ◽  
First Time ◽  
Do So

This paper deals with the stationary distribution of the virtual waiting time, i.e. the time between the arrival and the beginning of service of a customer in a single-server queue that operates as follows. If the server is busy at an arrival time, the customer is rejected. This customer attempts service again after some random delay and continues to do so until the first time at which the server is idle. At this time, the customer is served and leaves the system after service completion. Interarrival times and delays are assumed to be two independent sequences of i.i.d. exponentially distributed random variables. Service times are also i.i.d., generally distributed, and independent of the previous sequences.

On the virtual waiting time in an M/G/1 retrial queue

1991 ◽  
Vol 28 (02) ◽  
pp. 446-460 ◽  
Author(s):  
G. Falin ◽  
C. Fricker
Keyword(s):  
Waiting Time ◽  
Arrival Time ◽  
Retrial Queue ◽  
Single Server ◽  
Random Delay ◽  
Single Server Queue ◽  
Virtual Waiting Time ◽  
Server Queue ◽  
First Time ◽  
Do So

This paper deals with the stationary distribution of the virtual waiting time, i.e. the time between the arrival and the beginning of service of a customer in a single-server queue that operates as follows. If the server is busy at an arrival time, the customer is rejected. This customer attempts service again after some random delay and continues to do so until the first time at which the server is idle. At this time, the customer is served and leaves the system after service completion. Interarrival times and delays are assumed to be two independent sequences of i.i.d. exponentially distributed random variables. Service times are also i.i.d., generally distributed, and independent of the previous sequences.

On a single-server queue with group arrivals

1976 ◽  
Vol 13 (03) ◽  
pp. 619-622 ◽  
Author(s):  
J. W. Cohen
Keyword(s):  
Waiting Time ◽  
Queueing System ◽  
Limiting Distribution ◽  
Single Server ◽  
Waiting Time Distribution ◽  
Single Server Queue ◽  
Regenerative Processes ◽  
Virtual Waiting Time ◽  
Server Queue ◽  
Individual Service

The queueing system GI/G/1 with group arrivals and individual service of the customers is considered. For the stable situation the limiting distribution of the waiting time distribution of the kth served customer for k → ∞ is derived by using the theory of regenerative processes. It is assumed that the group sizes are i.i.d. variables of which the distribution is aperiodic. The relation between this limiting distribution and the stationary distribution of the virtual waiting time is derived.

On a single-server queue with group arrivals

1976 ◽  
Vol 13 (3) ◽  
pp. 619-622 ◽  
Author(s):  
J. W. Cohen
Keyword(s):  
Waiting Time ◽  
Queueing System ◽  
Limiting Distribution ◽  
Single Server ◽  
Waiting Time Distribution ◽  
Single Server Queue ◽  
Regenerative Processes ◽  
Virtual Waiting Time ◽  
Server Queue ◽  
Individual Service

The queueing system GI/G/1 with group arrivals and individual service of the customers is considered. For the stable situation the limiting distribution of the waiting time distribution of the kth served customer for k → ∞ is derived by using the theory of regenerative processes. It is assumed that the group sizes are i.i.d. variables of which the distribution is aperiodic. The relation between this limiting distribution and the stationary distribution of the virtual waiting time is derived.

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.

Decomposition property in a discrete-time queue with multiple input streams and service interruptions

2004 ◽  
Vol 41 (02) ◽  
pp. 524-534
Author(s):  
Fumio Ishizaki
Keyword(s):  
Discrete Time ◽  
Waiting Time ◽  
Stochastic Decomposition ◽  
Single Server ◽  
Single Server Queue ◽  
General Process ◽  
Decomposition Property ◽  
Service Interruptions ◽  
Virtual Waiting Time ◽  
Server Queue

This paper studies a discrete-time single-server queue with two independent inputs and service interruptions. One of the inputs to the queue is an independent and identically distributed process. The other is a much more general process and it is not required to be Markov nor is it required to be stationary. The service interruption process is also general and it is not required to be Markov or to be stationary. This paper shows that a stochastic decomposition property for the virtual waiting-time process holds in the discrete-time single-server queue with service interruptions. To the best of the author's knowledge, no stochastic decomposition results for virtual waiting-time processes in non-work-conserving queues, such as queues with service interruptions, have been obtained before and only work-conserving queues have been studied in the literature.

Decomposition property in a discrete-time queue with multiple input streams and service interruptions

2004 ◽  
Vol 41 (2) ◽  
pp. 524-534 ◽  
Author(s):  
Fumio Ishizaki
Keyword(s):  
Discrete Time ◽  
Waiting Time ◽  
Stochastic Decomposition ◽  
Single Server ◽  
Single Server Queue ◽  
General Process ◽  
Decomposition Property ◽  
Service Interruptions ◽  
Virtual Waiting Time ◽  
Server Queue

This paper studies a discrete-time single-server queue with two independent inputs and service interruptions. One of the inputs to the queue is an independent and identically distributed process. The other is a much more general process and it is not required to be Markov nor is it required to be stationary. The service interruption process is also general and it is not required to be Markov or to be stationary. This paper shows that a stochastic decomposition property for the virtual waiting-time process holds in the discrete-time single-server queue with service interruptions. To the best of the author's knowledge, no stochastic decomposition results for virtual waiting-time processes in non-work-conserving queues, such as queues with service interruptions, have been obtained before and only work-conserving queues have been studied in the literature.

On the single server queue with preemptive service interruptions

1971 ◽  
Vol 8 (4) ◽  
pp. 835-837 ◽  
Author(s):  
İzzet Şahin
Keyword(s):  
Integral Equation ◽  
Waiting Time ◽  
Stochastic System ◽  
Single Server ◽  
Single Server Queue ◽  
Service Interruptions ◽  
Time Problem ◽  
Server Queue ◽  
Waiting Time Problem ◽  
Limiting Behaviour

In [4], the limiting behaviour of a stochastic system with two types of input was investigated by reducing the problem to the solution of an integral equation. In this note we use the same approach to study the equilibrium waiting time problem for the general single server queue with preemptive service interruptions. (For a comprehensive account of the existing literature on queues with service interruptions we refer to [2] and [3].)

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