scholarly journals SOJOURN TIMES IN THE M/G/1 FB QUEUE WITH LIGHT-TAILED SERVICE TIMES

2005 ◽  
Vol 19 (3) ◽  
pp. 351-361 ◽  
Author(s):  
M. Mandjes ◽  
M. Nuyens
Keyword(s):  
Decay Rate ◽  
Sojourn Time ◽  
Busy Period ◽  
Service Discipline ◽  
Asymptotic Decay ◽  
Sojourn Times ◽  
Service Times ◽  
Asymptotic Decay Rate

The asymptotic decay rate of the sojourn time of a customer in the stationary M/G/1 queue under the foreground–background (FB) service discipline is studied. The FB discipline gives service to those customers that have received the least service so far. We prove that for light-tailed service times, the decay rate of the sojourn time is equal to the decay rate of the busy period. It is shown that FB minimizes the decay rate in the class of work-conserving disciplines.

Logarithmic asymptotics for steady-state tail probabilities in a single-server queue

1994 ◽  
Vol 31 (A) ◽  
pp. 131-156 ◽  
Author(s):  
Peter W. Glynn ◽  
Ward Whitt
Keyword(s):  
Steady State ◽  
Decay Rate ◽  
Partial Sums ◽  
Asymptotic Result ◽  
Service Discipline ◽  
Single Server ◽  
Single Server Queue ◽  
Asymptotic Decay ◽  
Server Queue ◽  
Service Times

We consider the standard single-server queue with unlimited waiting space and the first-in first-out service discipline, but without any explicit independence conditions on the interarrival and service times. We find conditions for the steady-state waiting-time distribution to have asymptotics of the form x–1 log P(W> x) → –θ ∗as x → ∞for θ ∗ > 0. We require only stationarity of the basic sequence of service times minus interarrival times and a Gärtner–Ellis condition for the cumulant generating function of the associated partial sums, i.e. n–1 log E exp (θSn) → ψ (θ) as n → ∞, plus regularity conditions on the decay rate function ψ. The asymptotic decay rate θ is the root of the equation ψ (θ) = 0. This result in turn implies a corresponding asymptotic result for the steady-state workload in a queue with general non-decreasing input. This asymptotic result covers the case of multiple independent sources, so that it provides additional theoretical support for a concept of effective bandwidths for admission control in multiclass queues based on asymptotic decay rates.

Logarithmic asymptotics for steady-state tail probabilities in a single-server queue

1994 ◽  
Vol 31 (A) ◽  
pp. 131-156 ◽  
Author(s):  
Peter W. Glynn ◽  
Ward Whitt
Keyword(s):  
Steady State ◽  
Decay Rate ◽  
Partial Sums ◽  
Asymptotic Result ◽  
Service Discipline ◽  
Single Server ◽  
Single Server Queue ◽  
Asymptotic Decay ◽  
Server Queue ◽  
Service Times

We consider the standard single-server queue with unlimited waiting space and the first-in first-out service discipline, but without any explicit independence conditions on the interarrival and service times. We find conditions for the steady-state waiting-time distribution to have asymptotics of the form x –1 log P(W > x) → –θ ∗as x → ∞for θ ∗ > 0. We require only stationarity of the basic sequence of service times minus interarrival times and a Gärtner–Ellis condition for the cumulant generating function of the associated partial sums, i.e. n –1 log E exp (θSn ) → ψ (θ) as n → ∞, plus regularity conditions on the decay rate function ψ. The asymptotic decay rate θ is the root of the equation ψ (θ) = 0. This result in turn implies a corresponding asymptotic result for the steady-state workload in a queue with general non-decreasing input. This asymptotic result covers the case of multiple independent sources, so that it provides additional theoretical support for a concept of effective bandwidths for admission control in multiclass queues based on asymptotic decay rates.

The dependence of sojourn times on service times in tandem queues

1984 ◽  
Vol 21 (3) ◽  
pp. 661-667 ◽  
Author(s):  
Xi-Ren Cao
Keyword(s):  
Sojourn Time ◽  
Past History ◽  
Interarrival Time ◽  
Conditional Probabilities ◽  
Tandem Queues ◽  
Sojourn Times ◽  
Distributed Service ◽  
Service Times

In this paper we study a series of servers with exponentially distributed service times. We find that the sojourn time of a customer at any server depends on the customer's past history only through the customer's interarrival time to that server. A method of calculating the conditional probabilities of sojourn times is developed.

ASYMPTOTIC PROPERTIES OF SOJOURN TIMES IN MULTICLASS TIME-SHARED SYSTEMS

2008 ◽  
Vol 22 (2) ◽  
pp. 231-259
Author(s):  
Arzad A. Kherani
Keyword(s):  
Sojourn Time ◽  
Busy Period ◽  
Asymptotic Properties ◽  
Tail Behavior ◽  
Queuing Systems ◽  
Conditional Mean ◽  
Sojourn Times ◽  
Heavy Tailed ◽  
Expected Sojourn Time ◽  
Residual Processing

We consider two multiclass discriminatory process sharing (DPS)-like time-shared M/G/1 queuing systems in which the weight assigned to a customer is a function of its class as well as (1) the attained service of the customer in the first system and (2) the residual processing time of the customer in the second system. We study the asymptotic slowdown, the ratio of expected sojourn time to the service requirement, of customers with very large service requirements. We also provide various results dealing with ordering of conditional mean sojourn times of any two given classes. We also show that the sojourn time of an arbitrary customer of a particular class in the standard DPS system (static weights) with heavy-tailed service requirements has a tail behavior similar to that of a customer from the same class that starts a busy period.

The dependence of sojourn times on service times in tandem queues

1984 ◽  
Vol 21 (03) ◽  
pp. 661-667
Author(s):  
Xi-Ren Cao
Keyword(s):  
Sojourn Time ◽  
Past History ◽  
Interarrival Time ◽  
Conditional Probabilities ◽  
Tandem Queues ◽  
Sojourn Times ◽  
Distributed Service ◽  
Service Times

In this paper we study a series of servers with exponentially distributed service times. We find that the sojourn time of a customer at any server depends on the customer's past history only through the customer's interarrival time to that server. A method of calculating the conditional probabilities of sojourn times is developed.

ASYMPTOTIC DECAY TOWARD THE PLANAR RAREFACTION WAVES OF SOLUTIONS FOR VISCOUS CONSERVATION LAWS IN SEVERAL SPACE DIMENSIONS

1996 ◽  
Vol 06 (03) ◽  
pp. 315-338 ◽  
Author(s):  
KAZUO ITO
Keyword(s):  
Conservation Laws ◽  
Decay Rate ◽  
Energy Method ◽  
Rarefaction Waves ◽  
Asymptotic Decay ◽  
One Dimensional ◽  
Viscous Conservation Laws ◽  
Asymptotic Decay Rate

This paper gives the asymptotic decay rate toward the planar rarefaction waves of the solutions for the scalar viscous conservation laws in two or more space dimensions. This is proved by a result on the decay rate of solutions for one-dimensional scalar viscous conservation laws and by using an L2-energy method with a weight of time.

Sojourn times and the overtaking condition in Jacksonian networks

1980 ◽  
Vol 12 (04) ◽  
pp. 1000-1018 ◽  
Author(s):  
J. Walrand ◽  
P. Varaiya
Keyword(s):  
Sojourn Time ◽  
Sojourn Times ◽  
Mutually Independent

Consider an open multiclass Jacksonian network in equilibrium and a path such that a customer travelling along it cannot be overtaken directly by a subsequent arrival or by the effects of subsequent arrivals. Then the sojourn times of this customer in the nodes constituting the path are all mutually independent and so the total sojourn time is easily calculated. Two examples are given to suggest that the non-overtaking condition may be necessary to ensure independence when there is a single customer class.

ASYMPTOTIC DECAY TOWARD THE PLANAR RAREFACTION WAVES FOR A MODEL SYSTEM OF THE RADIATING GAS IN TWO DIMENSIONS

2008 ◽  
Vol 18 (04) ◽  
pp. 511-541 ◽  
Author(s):  
WENLIANG GAO ◽  
CHANGJIANG ZHU
Keyword(s):  
Cauchy Problem ◽  
Maximum Principle ◽  
Coupled System ◽  
Model System ◽  
Two Dimensions ◽  
Rarefaction Waves ◽  
Asymptotic Decay ◽  
The Maximum Principle ◽  
The Cauchy Problem ◽  
Asymptotic Decay Rate

In this paper, we consider the asymptotic decay rate towards the planar rarefaction waves to the Cauchy problem for a hyperbolic–elliptic coupled system called as a model system of the radiating gas in two dimensions. The analysis based on the standard L2-energy method, L1-estimate and the monotonicity of profile obtained by the maximum principle.

Cumulative constrained sojourn times in semi-Markov processes with an application to pensionable service

1978 ◽  
Vol 15 (3) ◽  
pp. 531-542 ◽  
Author(s):  
Izzet Sahin
Keyword(s):  
Markov Processes ◽  
Sojourn Time ◽  
Working Life ◽  
Partial Coverage ◽  
Sojourn Times ◽  
Semi Markov Processes

This paper is concerned with the characterization of the cumulative pensionable service over an individual's working life that is made up of random lengths of service in different employments in a given industry, under partial coverage, transferability, and a uniform vesting rule. This characterization uses some results that are developed in the paper involving a functional and cumulative constrained sojourn times (constrained in the sense that if a sojourn time is less than a given constant it is not counted) in semi-Markov processes.

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