Recurrent emptiness in a finite queue with increasing arrival rate

1976 ◽  
Vol 13 (02) ◽  
pp. 423-426
Author(s):  
Stig I. Rosenlund
Keyword(s):  
Sufficient Conditions ◽  
Arrival Rate ◽  
Necessary And Sufficient Conditions ◽  
Single Server ◽  
Single Server Queue ◽  
Server Queue ◽  
Necessary And Sufficient

For a single-server queue with one waiting place and increasing arrival rate some necessary and sufficient conditions for infinitely many returns to emptiness with probability one are given.

Recurrent emptiness in a finite queue with increasing arrival rate

1976 ◽  
Vol 13 (2) ◽  
pp. 423-426
Author(s):  
Stig I. Rosenlund
Keyword(s):  
Sufficient Conditions ◽  
Arrival Rate ◽  
Necessary And Sufficient Conditions ◽  
Single Server ◽  
Single Server Queue ◽  
Server Queue ◽  
Necessary And Sufficient

For a single-server queue with one waiting place and increasing arrival rate some necessary and sufficient conditions for infinitely many returns to emptiness with probability one are given.

Asymptotic behavior of a multiplexer fed by a long-range dependent process

1999 ◽  
Vol 36 (01) ◽  
pp. 105-118 ◽  
Author(s):  
Zhen Liu ◽  
Philippe Nain ◽  
Don Towsley ◽  
Zhi-Li Zhang
Keyword(s):  
Asymptotic Behavior ◽  
Lower Bounds ◽  
Lognormal Distribution ◽  
Arrival Rate ◽  
Upper Bounds ◽  
Single Server ◽  
Service Capacity ◽  
Single Server Queue ◽  
Input Process ◽  
Server Queue

In this paper we study the asymptotic behavior of the tail of the stationary backlog distribution in a single server queue with constant service capacity c, fed by the so-called M/G/∞ input process or Cox input process. Asymptotic lower bounds are obtained for any distribution G and asymptotic upper bounds are derived when G is a subexponential distribution. We find the bounds to be tight in some instances, e.g. when G corresponds to either the Pareto or lognormal distribution and c − ρ < 1, where ρ is the arrival rate at the buffer.

A monotonicity result for a single-server queue subject to a Markov-modulated Poisson process

1995 ◽  
Vol 32 (4) ◽  
pp. 1103-1111 ◽  
Author(s):  
Qing Du
Keyword(s):  
Poisson Process ◽  
Arrival Rate ◽  
Loss Probability ◽  
Arrival Process ◽  
Single Server ◽  
Single Server Queue ◽  
Markov Modulated Poisson Process ◽  
Server Queue ◽  
Monotonicity Result ◽  
Markov Modulated

Consider a single-server queue with zero buffer. The arrival process is a three-level Markov modulated Poisson process with an arbitrary transition matrix. The time the system remains at level i (i = 1, 2, 3) is exponentially distributed with rate cα i. The arrival rate at level i is λ i and the service time is exponentially distributed with rate μ i. In this paper we first derive an explicit formula for the loss probability and then prove that it is decreasing in the parameter c. This proves a conjecture of Ross and Rolski's for a single-server queue with zero buffer.

Waiting time and workload in queues with periodic Poisson input

1989 ◽  
Vol 26 (02) ◽  
pp. 390-397 ◽  
Author(s):  
Austin J. Lemoine
Keyword(s):  
Differential Equation ◽  
Waiting Time ◽  
Arrival Rate ◽  
Time Of Day ◽  
Single Server ◽  
Single Server Queue ◽  
Poisson Input ◽  
Service Distribution ◽  
Server Queue ◽  
General Service

This paper develops moment formulas for asymptotic workload and waiting time in a single-server queue with periodic Poisson input and general service distribution. These formulas involve the corresponding moments of waiting-time (workload) for the M/G/1 system with the same average arrival rate and service distribution. In certain cases, all the terms in the formulas can be computed exactly, including moments of workload at each ‘time of day.' The approach makes use of an asymptotic version of the Takács [12] integro-differential equation, together with representation results of Harrison and Lemoine [3] and Lemoine [6].

A monotonicity result for a single-server queue subject to a Markov-modulated Poisson process

1995 ◽  
Vol 32 (04) ◽  
pp. 1103-1111 ◽  
Author(s):  
Qing Du
Keyword(s):  
Poisson Process ◽  
Arrival Rate ◽  
Loss Probability ◽  
Arrival Process ◽  
Single Server ◽  
Single Server Queue ◽  
Markov Modulated Poisson Process ◽  
Server Queue ◽  
Monotonicity Result ◽  
Markov Modulated

Consider a single-server queue with zero buffer. The arrival process is a three-level Markov modulated Poisson process with an arbitrary transition matrix. The time the system remains at level i (i = 1, 2, 3) is exponentially distributed with rate cα i . The arrival rate at level i is λ i and the service time is exponentially distributed with rate μ i . In this paper we first derive an explicit formula for the loss probability and then prove that it is decreasing in the parameter c. This proves a conjecture of Ross and Rolski's for a single-server queue with zero buffer.

scholarly journals The Benefit of Information in a Single-server Queue with Heterogeneous Service Valuations [Abstract]

10.28945/4356 ◽  
2019 ◽  
Keyword(s):  
Queue Length ◽  
Queuing Theory ◽  
Arrival Rate ◽  
Future Research ◽  
Single Server ◽  
Single Server Queue ◽  
Travel Costs ◽  
Control Of Queues ◽  
Server Queue ◽  
Heterogeneous Service

Aim/Purpose: How does heterogeneous valuation of service affect optimal control of queues? Background We analyze this heterogeneity by adding a component of travel costs, which differ with distance from the service point. Methodology: Mathematical analysis of queuing theory. Analyzing the anarchy function. Contribution: Enabling consumers to make optimal choices based on knowledge about their status, and enabling better control of the organizer. Findings: In the arrival rate is bounded, there is no need of interference. If it is unbounded then in many cases the organizer should impose the socially optimal queue length. Recommendations for Practitioners: In the arrival rate is bounded, there is no need of interference. If it is unbounded then in many cases the organizer should impose the socially optimal queue length. Recommendations for Researchers: Explore the following points: What happens when there are more than one server, located at different point. How should consumers behave, and what is the best way to locate service points. Impact on Society: Handling queues taking into account social welfare. Future Research: What happens when there are more than one server, located at different point. How should consumers behave, and what is the best way to locate service points.

Waiting time and workload in queues with periodic Poisson input

1989 ◽  
Vol 26 (2) ◽  
pp. 390-397 ◽  
Author(s):  
Austin J. Lemoine
Keyword(s):  
Differential Equation ◽  
Waiting Time ◽  
Arrival Rate ◽  
Time Of Day ◽  
Single Server ◽  
Single Server Queue ◽  
Poisson Input ◽  
Service Distribution ◽  
Server Queue ◽  
General Service

This paper develops moment formulas for asymptotic workload and waiting time in a single-server queue with periodic Poisson input and general service distribution. These formulas involve the corresponding moments of waiting-time (workload) for the M/G/1 system with the same average arrival rate and service distribution. In certain cases, all the terms in the formulas can be computed exactly, including moments of workload at each ‘time of day.' The approach makes use of an asymptotic version of the Takács [12] integro-differential equation, together with representation results of Harrison and Lemoine [3] and Lemoine [6].

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