Optimization of road design via the use of a queueing model with transit and local users and processor sharing discipline

A queueing model of considerable interest in computer engineering is the processor-sharing model in which the server shares its fixed capacity equally among all units present in the system. Here, we derive the mean and the variance of the equilibrium sojourn time, and deduce that the variance of the sojourn time is larger for the processor-sharing model than for the corresponding FCFS model.

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The sojourn time in the GI/M/1 queue by processor sharing

Journal of Applied Probability ◽

10.1017/s0021900200024827 ◽

1984 ◽

Vol 21 (02) ◽

pp. 437-442

Author(s):

V. Ramaswami

Keyword(s):

Sojourn Time ◽

Queueing Model ◽

Processor Sharing ◽

Computer Engineering ◽

The Mean

A queueing model of considerable interest in computer engineering is the processor-sharing model in which the server shares its fixed capacity equally among all units present in the system. Here, we derive the mean and the variance of the equilibrium sojourn time, and deduce that the variance of the sojourn time is larger for the processor-sharing model than for the corresponding FCFS model.

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Analysis of a multi-server queueing model of ABR

Journal of Applied Mathematics and Stochastic Analysis ◽

10.1155/s1048953398000288 ◽

1998 ◽

Vol 11 (3) ◽

pp. 339-354 ◽

Cited By ~ 10

Author(s):

R. Núñez-Queija ◽

O. J. Boxma

Keyword(s):

Asynchronous Transfer Mode ◽

Fixed Number ◽

Atm Networks ◽

Single Server ◽

Queueing Model ◽

Processor Sharing ◽

Preemptive Priority ◽

Transfer Mode ◽

Multi Server ◽

Channel Service

In this paper we present a queueing model for the performance analysis of Available Bit Rate (ABR) traffic in Asynchronous Transfer Mode (ATM) networks. We consider a multi-channel service station with two types of customers, denoted by high priority and low priority customers. In principle, high priority customers have preemptive priority over low priority customers, except on a fixed number of channels that are reserved for low priority traffic. The arrivals occur according to two independent Poisson processes, and service times are assumed to be exponentially distributed. Each high priority customer requires a single server, whereas low priority customers are served in processor sharing fashion. We derive the joint distribution of the numbers of customers (of both types) in the system in steady state. Numerical results illustrate the effect of high priority traffic on the service performance of low priority traffic.

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