Scaling Limits of a Tandem Retrial Queue with Common Orbit and Poisson Arrival Process

2021 ◽  
pp. 240-250
Author(s):  
Anatoly Nazarov ◽  
Svetlana Paul ◽  
Tuan Phung-Duc ◽  
Mariya Morozova
Keyword(s):  
Retrial Queue ◽  
Arrival Process ◽  
Scaling Limits ◽  
Poisson Arrival ◽  
Poisson Arrival Process

Analysis of Tandem Retrial Queue with Common Orbit and Poisson Arrival Process

2021 ◽  
pp. 441-456
Author(s):  
Anatoly Nazarov ◽  
Svetlana Paul ◽  
Tuan Phung-Duc ◽  
Mariya Morozova
Keyword(s):  
Retrial Queue ◽  
Arrival Process ◽  
Poisson Arrival ◽  
Poisson Arrival Process

The departure process from a queueing system

1976 ◽  
Vol 80 (2) ◽  
pp. 283-285 ◽  
Author(s):  
F. P. Kelly
Keyword(s):  
Queueing System ◽  
Arrival Process ◽  
Single Server ◽  
Departure Process ◽  
Common Distribution ◽  
Poisson Arrival ◽  
Queue Discipline ◽  
Common Distribution Function ◽  
Image Position ◽  
Poisson Arrival Process

Consider a single-server queueing system with a Poisson arrival process at rate λ and positive service requirements independently distributed with common distribution function B(z) and finite expectationwhere βλ < 1, i.e. an M/G/1 system. When the queue discipline is first come first served, or last come first served without pre-emption, the stationary departure process is Poisson if and only if G = M (i.e. B(z) = 1 − exp (−z/β)); see (8), (4) and (2). In this paper it is shown that when the queue discipline is last come first served with pre-emption the stationary departure process is Poisson whatever the form of B(z). The method used is adapted from the approach of Takács (10) and Shanbhag and Tambouratzis (9).

A time-varying Poisson arrival process generator

SIMULATION ◽  
1984 ◽  
Vol 43 (4) ◽  
pp. 193-195 ◽  
Author(s):  
Robert W. Klein ◽  
Stephen D. Roberts
Keyword(s):  
Arrival Process ◽  
Time Varying ◽  
Poisson Arrival ◽  
Poisson Arrival Process

Two sufficient properties for the insensitivity of a class of queueing models

1991 ◽  
Vol 28 (03) ◽  
pp. 664-672
Author(s):  
Moshe Haviv
Keyword(s):  
Arrival Process ◽  
Queueing Models ◽  
Sufficient Condition ◽  
Poisson Arrival ◽  
System 2 ◽  
Poisson Arrival Process

For indivisible strong work-conserving queueing models with a Poisson arrival process, each of the following two properties is a sufficient condition for insensitivity. (1) The completed workload of a job receiving service is independent of the number of jobs in the system. (2) Independently of the completed workloads of the jobs in the system, they all are equally likely to be in service. For models which additionally belong to the class described by two families of parameters each of these properties is also necessary for insensitivity.

The asymptotic behavior o queues with time-varying arrival rates

1984 ◽  
Vol 21 (01) ◽  
pp. 143-156 ◽  
Author(s):  
Daniel P. Heyman ◽  
Ward Whitt
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Stability ◽  
Limit Theorems ◽  
Arrival Process ◽  
Periodic Case ◽  
Time Varying ◽  
Poisson Arrival ◽  
Poisson Arrival Process

This paper discusses the asymptotic behavior of the Mt/G/c queue having a Poisson arrival process with a general deterministic intensity. Since traditional equilibrium does not always exist, other notions of asymptotic stability are introduced and investigated. For the periodic case, limit theorems are proved complementing Harrison and Lemoine (1977) and Lemoine (1981).

An analysis of the fixed-cycle traffic-light problem

1981 ◽  
Vol 18 (03) ◽  
pp. 672-683 ◽  
Author(s):  
Richard Cowan
Keyword(s):  
Arrival Process ◽  
Traffic Light ◽  
Traffic Lights ◽  
Poisson Arrival ◽  
Pass Through ◽  
Poisson Arrival Process

A realistic non-Poisson arrival process is used in a model for intersections controlled by fixed-cycle traffic lights. Average delays, queue sizes and percentage of delayed vehicles are derived. The distribution of the number of vehicles which pass through during the green phases is found. Certain model anomalies which are inherent in earlier work are eliminated by the use of this model.

Light traffic approximations in many-server queues

1992 ◽  
Vol 24 (01) ◽  
pp. 202-218 ◽  
Author(s):  
D. J. Daley ◽  
T. Rolski
Keyword(s):  
Waiting Time ◽  
Arrival Process ◽  
Light Traffic ◽  
Traffic Conditions ◽  
Poisson Arrival ◽  
Many Server Queues ◽  
Special Case ◽  
Poisson Arrival Process

This paper complements two previous studies (Daley and Rolski (1984), (1991)) by investigating limit properties of the waiting time in k-server queues with renewal arrival process under ‘light traffic' conditions. Formulae for the limits of the probability of waiting and the waiting time moments are derived for the two approaches of dilation and thinning of the arrival process. Asmussen's (1991) approach to light traffic limits applies to the cases considered, of which the Poisson arrival process (i.e. M/G/k) is a special case and for which formulae are given.

An analysis of the fixed-cycle traffic-light problem

1981 ◽  
Vol 18 (3) ◽  
pp. 672-683 ◽  
Author(s):  
Richard Cowan
Keyword(s):  
Arrival Process ◽  
Traffic Light ◽  
Traffic Lights ◽  
Poisson Arrival ◽  
Pass Through ◽  
Poisson Arrival Process

A realistic non-Poisson arrival process is used in a model for intersections controlled by fixed-cycle traffic lights. Average delays, queue sizes and percentage of delayed vehicles are derived. The distribution of the number of vehicles which pass through during the green phases is found. Certain model anomalies which are inherent in earlier work are eliminated by the use of this model.

scholarly journals A Continuous-Time Approach to Robbins' Problem of Minimizing the Expected Rank

2009 ◽  
Vol 46 (01) ◽  
pp. 1-18 ◽  
Author(s):  
F. Thomas Bruss ◽  
Yvik C. Swan
Keyword(s):  
Continuous Time ◽  
Value Function ◽  
Independent Random Variables ◽  
Arrival Process ◽  
Optimal Selection ◽  
Lipschitz Continuous ◽  
Poisson Arrival ◽  
Alternative Approach ◽  
Limiting Value ◽  
Poisson Arrival Process

Let X 1, X 2, …, X n be independent random variables uniformly distributed on [0,1]. We observe these sequentially and have to stop on exactly one of them. No recall of preceding observations is permitted. What stopping rule minimizes the expected rank of the selected observation? What is the value of the expected rank (as a function of n) and what is the limit of this value when n goes to ∞? This full-information expected selected-rank problem is known as Robbins' problem of minimizing the expected rank, and its general solution is unknown. In this paper we provide an alternative approach to Robbins' problem. Our model is similar to that of Gnedin (2007). For this, we consider a continuous-time version of the problem in which the observations follow a Poisson arrival process on ℝ+ × [0,1] of homogeneous rate 1. Translating the previous optimal selection problem in this setting, we prove that, under reasonable assumptions, the corresponding value function w (t) is bounded and Lipschitz continuous. Our main result is that the limiting value of the Poisson embedded problem exists and is equal to that of Robbins' problem. We prove that w (t) is differentiable and also derive a differential equation for this function. Although we have not succeeded in using this equation to improve on bounds on the optimal limiting value, we argue that it has this potential.

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