scholarly journals Heavy traffic limit theorems for a queue with Poisson ON/OFF long-range dependent sources and general service time distribution

2012 ◽  
Vol 28 (4) ◽  
pp. 807-822 ◽  
Author(s):  
Wan-yang Dai
Keyword(s):  
Long Range ◽  
Service Time ◽  
Time Distribution ◽  
Limit Theorems ◽  
Heavy Traffic ◽  
Service Time Distribution ◽  
Heavy Traffic Limit ◽  
Dependent Sources ◽  
General Service

On the GA/G/∞ queue

1983 ◽  
Vol 15 (2) ◽  
pp. 444-459 ◽  
Author(s):  
Thomas Kuczek
Keyword(s):  
Service Time ◽  
Limit Theorems ◽  
Regularity Condition ◽  
Heavy Traffic ◽  
Arrival Process ◽  
Life Situation ◽  
Random Measures ◽  
Server Queue ◽  
Traffic Theory ◽  
General Service

A particular queue, the general arrival, general service-time, infinite-server queue (GA/G/∞), is introduced and certain of its properties studied. Motivated by a life situation in which the interarrival times for service converge to 0, a different sort of regularity condition (involving a tail property of random measures) is imposed on the arrival process to prove various limit theorems. There are similarities to heavy-traffic theory.

The discrete-time single-server queue with time-inhomogeneous compound Poisson input and general service time distribution

1978 ◽  
Vol 15 (3) ◽  
pp. 590-601 ◽  
Author(s):  
Do Le Minh
Keyword(s):  
Discrete Time ◽  
Service Time ◽  
Time Distribution ◽  
Single Server ◽  
Service Time Distribution ◽  
Queueing Model ◽  
Compound Poisson ◽  
Poisson Input ◽  
Server Queue ◽  
General Service

This paper studies a discrete-time, single-server queueing model having a compound Poisson input with time-dependent parameters and a general service time distribution.All major transient characteristics of the system can be calculated very easily. For the queueing model with periodic arrival function, some explicit results are obtained.

The discrete-time single-server queue with time-inhomogeneous compound Poisson input and general service time distribution

1978 ◽  
Vol 15 (03) ◽  
pp. 590-601 ◽  
Author(s):  
Do Le Minh
Keyword(s):  
Discrete Time ◽  
Service Time ◽  
Time Distribution ◽  
Single Server ◽  
Service Time Distribution ◽  
Queueing Model ◽  
Compound Poisson ◽  
Poisson Input ◽  
Server Queue ◽  
General Service

This paper studies a discrete-time, single-server queueing model having a compound Poisson input with time-dependent parameters and a general service time distribution. All major transient characteristics of the system can be calculated very easily. For the queueing model with periodic arrival function, some explicit results are obtained.

scholarly journals An Analysis of a Close-Type Queuing System with General Service-Time Distribution

1970 ◽  
Vol 3 (1) ◽  
pp. 77-82
Author(s):  
Yoshio Yoshioka ◽  
Tomoyuki Nagase
Keyword(s):  
Service Time ◽  
Time Distribution ◽  
Probability Distributions ◽  
Queuing System ◽  
Multiprocessor System ◽  
Service Time Distribution ◽  
Systems Model ◽  
Proposed Model ◽  
Repair Procedure ◽  
General Service

This paper presents an innovative approach to solve probability distributions of a close feed back loop type queuing system with general service time distribution. This model is applied to a multiprocessor system where some of its nodes are performed a repair procedure during a nodes malfunction condition. Our model is appropriate for a multiprocessor system that employs a common bus or for a multi-node system in computer networks. A meticulous analysis of the systems model has been conducted and numerical results have been obtained to scrutinize the proposed model.

scholarly journals A heavy-traffic theorem for the GI/G/1 queue with a Pareto-type service time distribution

1998 ◽  
Vol 11 (3) ◽  
pp. 247-254 ◽  
Author(s):  
J. W. Cohen
Keyword(s):  
Service Time ◽  
Time Distribution ◽  
Heavy Traffic ◽  
Asymptotic Series ◽  
Traffic Load ◽  
Interarrival Time ◽  
Service Time Distribution ◽  
Tail Probabilities ◽  
S Transform ◽  
Stationary Waiting Time

For the GI/G/1 queueing model with traffic load a<1, service time distribution B(t) and interarrival time distribution A(t), whenever for t→∞1−B(t)∼c(t/β)ν+O(e−δt),c>0,1<ν<2,δ>0, and ∫0∞tμdA(t)<∞ for μ>ν, (1−a)1ν−1w converges in distribution for a↑1. Here w is distributed as the stationary waiting time distribution. The L.-S. transform of the limiting distribution is derived and an asymptotic series for its tail probabilities is obtained. The theorem actually proved in the text concerns a slightly more general asymptotic behavior of 1−B(t), t→∞, than mentioned above.

scholarly journals Buffer Overflow Period in a MAP Queue

2007 ◽  
Vol 2007 ◽  
pp. 1-18 ◽  
Author(s):  
Andrzej Chydzinski
Keyword(s):  
Service Time ◽  
Time Distribution ◽  
Markovian Arrival Process ◽  
Numerical Calculations ◽  
Buffer Overflow ◽  
Arrival Process ◽  
Service Time Distribution ◽  
Process Map ◽  
General Service ◽  
Number Of Cells

The buffer overflow period in a queue with Markovian arrival process (MAP) and general service time distribution is investigated. The results include distribution of the overflow period in transient and stationary regimes and the distribution of the number of cells lost during the overflow interval. All theorems are illustrated via numerical calculations.

Sign in / Sign up

Export Citation Format

Share Document