Approximations for delays using asymptotic estimates

1984 ◽  
Vol 16 (1) ◽  
pp. 6-6
Author(s):  
David Y. Burman ◽  
Donald R. Smith
Keyword(s):  
Markov Process ◽  
Poisson Process ◽  
Heavy Traffic ◽  
Single Server ◽  
Asymptotic Estimates ◽  
Single Server Queue ◽  
Average Delay ◽  
Multiserver Queues ◽  
Server Queue

Consider a general single-server queue where the customers arrive according to a Poisson process whose rate is modulated according to an independent Markov process. The authors have previously reported on limits for the average delay in light and heavy traffic. In this paper we review these results, extend them to multiserver queues, and describe some approximations obtained from them for general delays.

Approximations for delays using asymptotic estimates

1984 ◽  
Vol 16 (01) ◽  
pp. 6
Author(s):  
David Y. Burman ◽  
Donald R. Smith
Keyword(s):  
Markov Process ◽  
Poisson Process ◽  
Heavy Traffic ◽  
Single Server ◽  
Asymptotic Estimates ◽  
Single Server Queue ◽  
Average Delay ◽  
Multiserver Queues ◽  
Server Queue

Consider a general single-server queue where the customers arrive according to a Poisson process whose rate is modulated according to an independent Markov process. The authors have previously reported on limits for the average delay in light and heavy traffic. In this paper we review these results, extend them to multiserver queues, and describe some approximations obtained from them for general delays.

On ross's conjectures about queues with non-stationary poisson arrivals

1982 ◽  
Vol 19 (01) ◽  
pp. 245-249 ◽  
Author(s):  
D. P. Heyman
Keyword(s):  
Poisson Process ◽  
Arrival Process ◽  
Single Server ◽  
Single Server Queue ◽  
Average Delay ◽  
Server Queue ◽  
Poisson Arrivals

Ross (1978) conjectured that the average delay in a single-server queue is larger when the arrival process is a non-stationary Poisson process than when it is a stationary Poisson process with the same rate. We present an example where equality obtains. When the number of waiting-positions is finite, Ross conjectured that the proportion of lost customers is greater in the nonstationary case. We present a counterexample to this conjecture.

On ross's conjectures about queues with non-stationary poisson arrivals

1982 ◽  
Vol 19 (1) ◽  
pp. 245-249 ◽  
Author(s):  
D. P. Heyman
Keyword(s):  
Poisson Process ◽  
Arrival Process ◽  
Single Server ◽  
Single Server Queue ◽  
Average Delay ◽  
Server Queue ◽  
Poisson Arrivals

Ross (1978) conjectured that the average delay in a single-server queue is larger when the arrival process is a non-stationary Poisson process than when it is a stationary Poisson process with the same rate. We present an example where equality obtains. When the number of waiting-positions is finite, Ross conjectured that the proportion of lost customers is greater in the nonstationary case. We present a counterexample to this conjecture.

BROWNIAN MOTION MINUS THE INDEPENDENT INCREMENTS: REPRESENTATION AND QUEUING APPLICATION

2020 ◽  
pp. 1-25
Author(s):  
Kerry Fendick
Keyword(s):  
Brownian Motion ◽  
Maximum Likelihood ◽  
Markov Process ◽  
Maximum Likelihood Estimators ◽  
Single Server ◽  
Single Server Queue ◽  
Stationary Increments ◽  
Transient Distribution ◽  
Independent Increments ◽  
Server Queue

This paper relaxes assumptions defining multivariate Brownian motion (BM) to construct processes with dependent increments as tractable models for problems in engineering and management science. We show that any Gaussian Markov process starting at zero and possessing stationary increments and a symmetric smooth kernel has a parametric kernel of a particular form, and we derive the unique unbiased, jointly sufficient, maximum-likelihood estimators of those parameters. As an application, we model a single-server queue driven by such a process and derive its transient distribution conditional on its history.

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.

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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