scholarly journals Using simulation to study service-rate controls to stabilize performance in a single-server queue with time-varying arrival rate

2015 ◽  
Author(s):  
Ni Ma ◽  
Ward Whitt
Keyword(s):  
Arrival Rate ◽  
Service Rate ◽  
Single Server ◽  
Time Varying ◽  
Single Server Queue ◽  
Server Queue

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.

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.

The single-server queue with random service output

1975 ◽  
Vol 12 (04) ◽  
pp. 763-778 ◽  
Author(s):  
O. J. Boxma
Keyword(s):  
Service Process ◽  
Service Rate ◽  
Single Server ◽  
Queueing Model ◽  
Single Server Queue ◽  
Independent Increments ◽  
Server Queue ◽  
Work Done

In this paper a problem arising in queueing and dam theory is studied. We shall consider a G/G*/1 queueing model, i.e., a G/G/1 queueing model of which the service process is a separable centered process with stationary independent increments. This is a generalisation of the well-known G/G/1 model with constant service rate. Several results concerning the amount of work done by the server, the busy cycles etc., are derived, mainly using the well-known method of Pollaczek. Emphasis is laid on the similarities and dissimilarities between the results of the ‘classical’ G/G/1 model and the G/G*/1 model.

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].

Constrained Average Cost Markov Decision Chains

1993 ◽  
Vol 7 (1) ◽  
pp. 69-83 ◽  
Author(s):  
Linn I. Sennott
Keyword(s):  
Rate Control ◽  
Operating Cost ◽  
Service Rate ◽  
Single Server ◽  
Single Server Queue ◽  
Stationary Policy ◽  
Server Queue ◽  
Markov Decision ◽  
Average Operating ◽  
Holding Cost

A Markov decision chain with denumerable state space incurs two types of costs — for example, an operating cost and a holding cost. The objective is to minimize the expected average operating cost, subject to a constraint on the expected average holding cost. We prove the existence of an optimal constrained randomized stationary policy, for which the two stationary policies differ on at most one state. The examples treated are a packet communication system with reject option and a single-server queue with service rate control.

Single-Server Queue System of Shuttle Bus Performance: Federal University of Technology Akure as Case Study

2019 ◽  
Vol 5 (3) ◽  
pp. 9-14
Author(s):  
Sidiq Okwudili Ben
Keyword(s):  
Laplace Transform ◽  
Poisson Process ◽  
Service Rate ◽  
Single Server ◽  
Single Server Queue ◽  
Queue System ◽  
University Of Technology ◽  
Server Queue

This study has examined the performance of University transport bus shuttle based on utilization using a Single-server queue system which occur if arrival and service rate is Poisson distributed (single queue) (M/M/1) queue. In the methodology, Single-server queue system was modelled based on Poisson Process with the introduction of Laplace Transform. It is concluded that the performance of University transport bus shuttle is 96.6 percent which indicates a very good performance such that the supply of shuttle bus in FUTA is capable of meeting the demand.

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.

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