scholarly journals Queueing systems with many servers: Null controllability in heavy traffic

2006 ◽  
Vol 16 (4) ◽  
pp. 1764-1804 ◽  
Author(s):  
Rami Atar ◽  
Avi Mandelbaum ◽  
Gennady Shaikhet
Keyword(s):  
Heavy Traffic ◽  
Queueing Systems ◽  
Null Controllability

On a tandem queueing model with identical service times at both counters, II

1979 ◽  
Vol 11 (3) ◽  
pp. 644-659 ◽  
Author(s):  
O. J. Boxma
Keyword(s):  
Heavy Traffic ◽  
Queueing Systems ◽  
Single Server ◽  
Service Time Distribution ◽  
In Series ◽  
Mean And Variance ◽  
Queues In Series ◽  
The Mean ◽  
Service Times ◽  
Practical Implications

This paper is devoted to the practical implications of the theoretical results obtained in Part I [1] for queueing systems consisting of two single-server queues in series in which the service times of an arbitrary customer at both queues are identical. For this purpose some tables and graphs are included. A comparison is made—mainly by numerical and asymptotic techniques—between the following two phenomena: (i) the queueing behaviour at the second counter of the two-stage tandem queue and (ii) the queueing behaviour at a single-server queue with the same offered (Poisson) traffic as the first counter and the same service-time distribution as the second counter. This comparison makes it possible to assess the influence of the first counter on the queueing behaviour at the second counter. In particular we note that placing the first counter in front of the second counter in heavy traffic significantly reduces both the mean and variance of the total time spent in the second system.

Controlled queues in heavy traffic

1975 ◽  
Vol 7 (3) ◽  
pp. 656-671 ◽  
Author(s):  
John H. Rath
Keyword(s):  
Diffusion Process ◽  
Queue Length ◽  
Queueing System ◽  
Systems Approach ◽  
Heavy Traffic ◽  
Queueing Systems ◽  
Control Policy ◽  
Controlled Diffusion ◽  
Controlled Queues

This paper studies a controlled queueing system in which the decisionmaker may change servers according to rules which depend only on the queue length. It is proved that for a given control policy a properly normalised sequence of these controlled queue length processes converges weakly to a controlled diffusion process as the queueing systems approach a state of heavy traffic.

Drift Parameter Estimation for a Reflected Fractional Brownian Motion Based on its Local Time

2013 ◽  
Vol 50 (02) ◽  
pp. 592-597 ◽  
Author(s):  
Yaozhong Hu ◽  
Chihoon Lee
Keyword(s):  
Parameter Estimation ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Local Time ◽  
Heavy Traffic ◽  
Queueing Systems ◽  
Service Rate ◽  
Time Process ◽  
State Process ◽  
Drift Parameter

We consider a drift parameter estimation problem when the state process is a reflected fractional Brownian motion (RFBM) with a nonzero drift parameter and the observation is the associated local time process. The RFBM process arises as the key approximating process for queueing systems with long-range dependent and self-similar input processes, where the drift parameter carries the physical meaning of the surplus service rate and plays a central role in the heavy-traffic approximation theory for queueing systems. We study a statistical estimator based on the cumulative local time process and establish its strong consistency and asymptotic normality.

On a tandem queueing model with identical service times at both counters, II

1979 ◽  
Vol 11 (03) ◽  
pp. 644-659 ◽  
Author(s):  
O. J. Boxma
Keyword(s):  
Heavy Traffic ◽  
Queueing Systems ◽  
Single Server ◽  
Service Time Distribution ◽  
In Series ◽  
Mean And Variance ◽  
Queues In Series ◽  
The Mean ◽  
Service Times ◽  
Practical Implications

This paper is devoted to the practical implications of the theoretical results obtained in Part I [1] for queueing systems consisting of two single-server queues in series in which the service times of an arbitrary customer at both queues are identical. For this purpose some tables and graphs are included. A comparison is made—mainly by numerical and asymptotic techniques—between the following two phenomena: (i) the queueing behaviour at the second counter of the two-stage tandem queue and (ii) the queueing behaviour at a single-server queue with the same offered (Poisson) traffic as the first counter and the same service-time distribution as the second counter. This comparison makes it possible to assess the influence of the first counter on the queueing behaviour at the second counter. In particular we note that placing the first counter in front of the second counter in heavy traffic significantly reduces both the mean and variance of the total time spent in the second system.

Controlled queues in heavy traffic

1975 ◽  
Vol 7 (03) ◽  
pp. 656-671 ◽  
Author(s):  
John H. Rath
Keyword(s):  
Diffusion Process ◽  
Queue Length ◽  
Queueing System ◽  
Systems Approach ◽  
Heavy Traffic ◽  
Queueing Systems ◽  
Control Policy ◽  
Controlled Diffusion ◽  
Controlled Queues

This paper studies a controlled queueing system in which the decisionmaker may change servers according to rules which depend only on the queue length. It is proved that for a given control policy a properly normalised sequence of these controlled queue length processes converges weakly to a controlled diffusion process as the queueing systems approach a state of heavy traffic.

scholarly journals Economies-of-Scale in Many-Server Queueing Systems: Tutorial and Partial Review of the QED Halfin--Whitt Heavy-Traffic Regime

SIAM Review ◽  
2019 ◽  
Vol 61 (3) ◽  
pp. 403-440 ◽  
Author(s):  
Johan S. H. van Leeuwaarden ◽  
Britt W. J. Mathijsen ◽  
Bert Zwart
Keyword(s):  
Economies Of Scale ◽  
Heavy Traffic ◽  
Queueing Systems

A diffusion approximation for correlation in queues

1980 ◽  
Vol 17 (04) ◽  
pp. 1033-1047 ◽  
Author(s):  
C. M. Woodside ◽  
B. Pagurek ◽  
G. F. Newell
Keyword(s):  
Waiting Time ◽  
Probability Distributions ◽  
Heavy Traffic ◽  
Waiting Times ◽  
Queueing Systems ◽  
Spectral Density Function ◽  
Percentage Error ◽  
Similar Accuracy ◽  
System Time ◽  
Infinite Sum

A diffusion model is used to find heavy traffic approximate autocorrelation functions for several variables in queueing systems (i.e. for waiting time, system time, number in system and unfinished work). A table is given by which correlations can easily be found for each variable in anyGI/G/1 queue. Further, the infinite sum or integral of the autocorrelations is also found, and the spectral density function. The sum has applications in statistical analysis of queues.Extensive comparisons of approximate and exact correlations and their sums are reported, particularly for waiting times and system times, but also including number in system inM/M/1 queues. In general the correlations have similar accuracy to the probability distributions found by diffusion approximations. The percentage error is less for number in system than for waiting time.

scholarly journals A unified method to analyze overtake free queueing systems

1996 ◽  
Vol 28 (2) ◽  
pp. 588-625 ◽  
Author(s):  
Dimitris Bertsimas ◽  
Georgia Mourtzinou
Keyword(s):  
Heavy Traffic ◽  
Complete Solution ◽  
Queueing Systems ◽  
Exact Results ◽  
Traffic Conditions ◽  
Special Cases ◽  
Number Of Customers ◽  
First In First Out ◽  
Heavy Traffic Conditions ◽  
Unified Method

In this paper we demonstrate that the distributional laws that relate the number of customers in the system (queue), L(Q) and the time a customer spends in the system (queue), S(W) under the first-in-first-out (FIFO) discipline are special cases of the H = λG law and lead to a complete solution for the distributions of L, Q, S, W for queueing systems which satisfy distributional laws for both L and Q (overtake free systems). Moreover, in such systems the derivation of the distributions of L, Q, S, W can be done in a unified way. Consequences of the distributional laws include a generalization of PASTA to queueing systems with arbitrary renewal arrivals under heavy traffic conditions, a generalization of the Pollaczek–Khinchine formula to the G//G/1 queue, an extension of the Fuhrmann and Cooper decomposition for queues with generalized vacations under mixed generalized Erlang renewal arrivals, approximate results for the distributions of L, S in a GI/G/∞ queue, and exact results for the distributions of L, Q, S, W in priority queues with mixed generalized Erlang renewal arrivals.

Sign in / Sign up

Export Citation Format

Share Document