scholarly journals On the Transient Queue with the Dropping Function

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 825
Author(s):  
Andrzej Chydzinski
Keyword(s):  
Queueing System ◽  
Transient Behavior ◽  
Time Interval ◽  
Queue Size ◽  
Internet Routers ◽  
Management Schemes ◽  
Natural Characteristic ◽  
Dropping Function ◽  
Theoretical Results ◽  
Steady State Performance

We deal with a queueing system, in which arriving packets are being dropped with the probability depending on the queue size. Such a scheme is used in several active queue management schemes proposed for Internet routers. In this paper, we derive and analyze a selected transient characteristic of the model, i.e., the probability that in a given time interval the queue size is kept under a predefined level. As the main purpose of the discussed queueing scheme is to maintain the queue size low, this is a natural characteristic to study. In addition to that, the average time to reach a given level is derived. Theoretical results for both characteristics are accompanied by numerical examples. Among other things, they demonstrate that the transient behavior of the queue may vary significantly with the shape of the dropping function, even if the steady-state performance remains unaltered.

A relation between stationary queue and waiting time distributions

1971 ◽  
Vol 8 (03) ◽  
pp. 617-620 ◽  
Author(s):  
Rasoul Haji ◽  
Gordon F. Newell
Keyword(s):  
Waiting Time ◽  
Queueing System ◽  
Arrival Process ◽  
Time Interval ◽  
Queue Size ◽  
Random Time Interval ◽  
Queue Discipline ◽  
Stationary Waiting Time ◽  
Number Of Customers ◽  
First In First Out

A theorem is proved which, in essence, says the following. If, for any queueing system, (i) the arrival process is stationary, (ii) the queue discipline is first-in-first-out (FIFO), and (iii) the waiting time of each customer is statistically independent of the number of arrivals during any time interval after his arrival, then the stationary random queue size has the same distribution as the number of customers who arrive during a random time interval distributed as the stationary waiting time.

A relation between stationary queue and waiting time distributions

1971 ◽  
Vol 8 (3) ◽  
pp. 617-620 ◽  
Author(s):  
Rasoul Haji ◽  
Gordon F. Newell
Keyword(s):  
Waiting Time ◽  
Queueing System ◽  
Arrival Process ◽  
Time Interval ◽  
Queue Size ◽  
Random Time Interval ◽  
Queue Discipline ◽  
Stationary Waiting Time ◽  
Number Of Customers ◽  
First In First Out

A theorem is proved which, in essence, says the following. If, for any queueing system, (i) the arrival process is stationary, (ii) the queue discipline is first-in-first-out (FIFO), and (iii) the waiting time of each customer is statistically independent of the number of arrivals during any time interval after his arrival, then the stationary random queue size has the same distribution as the number of customers who arrive during a random time interval distributed as the stationary waiting time.

QLREDActive Queue Management Algorithm

2021 ◽  
Vol 28 (1) ◽  
Author(s):  
S.O. Hassan ◽  
A.O. Oluwatope ◽  
C. Ajaegbu ◽  
K-K.A. Abdullah ◽  
A.O. Olasupo
Keyword(s):  
Queue Size ◽  
Packet Dropping ◽  
Simulation Performance ◽  
Internet Routers ◽  
Dropping Probability ◽  
Management Algorithm ◽  
Traffic Loads ◽  
Probability Profile ◽  
Dropping Function ◽  
Minimal Effort

The Random Early Detection (RED) algorithm has not been successful in keeping the average queue size low. In this paper, we an improved RED-based algorithm called QLRED which divides the dropping probability function of the RED algorithm into two equal segments. The first segment utilises a quadratic packet dropping function while the second segment deploys a linear packet dropping function respectively so as to distinguish between light and high traffic loads. The ns-3 simulation performance evaluations clearly showed that QLRED algorithm effectively controls the average queue size under various network conditions resulting in a low delay. Replacing/upgrading the RED algorithm in Internet routers requires minimal effort since only the packet dropping probability profile needs to be adjusted.

The single-server queue with service depending on queue size and with the preemptive-resume last-come–first-served queue discipline

1987 ◽  
Vol 24 (03) ◽  
pp. 758-767
Author(s):  
D. Fakinos
Keyword(s):  
Queueing System ◽  
Limiting Distribution ◽  
Single Server ◽  
Queue Size ◽  
Single Server Queue ◽  
Preemptive Resume ◽  
Server Queue ◽  
Queue Discipline ◽  
Service Times

This paper studies theGI/G/1 queueing system assuming that customers have service times depending on the queue size and also that they are served in accordance with the preemptive-resume last-come–first-served queue discipline. Expressions are given for the limiting distribution of the queue size and the remaining durations of the corresponding services, when the system is considered at arrival epochs, at departure epochs and continuously in time. Also these results are applied to some particular cases of the above queueing system.

THE ALLOCATION OF CUSTOMERS IN A DISCRETE-TIME MULTI-SERVER QUEUEING SYSTEM

2010 ◽  
Vol 27 (06) ◽  
pp. 649-667 ◽  
Author(s):  
WEI SUN ◽  
NAISHUO TIAN ◽  
SHIYONG LI
Keyword(s):  
Performance Measures ◽  
Discrete Time ◽  
Queueing System ◽  
Arrival Rate ◽  
Allocation Problem ◽  
Optimal Outcome ◽  
The Subject ◽  
Multi Server ◽  
Theoretical Results

This paper, analyzes the allocation problem of customers in a discrete-time multi-server queueing system and considers two criteria for routing customers' selections: equilibrium and social optimization. As far as we know, there is no literature concerning the discrete-time multi-server models on the subject of equilibrium behaviors of customers and servers. Comparing the results of customers' distribution at the servers under the two criteria, we show that the servers used in equilibrium are no more than those used in the socially optimal outcome, that is, the individual's decision deviates from the socially preferred one. Furthermore, we also clearly show the mutative trend of several important performance measures for various values of arrival rate numerically to verify the theoretical results.

scholarly journals New Methods of Finite-Time Synchronization for a Class of Fractional-Order Delayed Neural Networks

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Weiwei Zhang ◽  
Jinde Cao ◽  
Ahmed Alsaedi ◽  
Fuad E. Alsaadi
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Finite Time ◽  
Time Synchronization ◽  
Sufficient Conditions ◽  
Time Interval ◽  
Finite Time Interval ◽  
Delayed Neural Networks ◽  
New Methods ◽  
Theoretical Results

Finite-time synchronization for a class of fractional-order delayed neural networks with fractional order α, 0<α≤1/2 and 1/2<α<1, is investigated in this paper. Through the use of Hölder inequality, generalized Bernoulli inequality, and inequality skills, two sufficient conditions are considered to ensure synchronization of fractional-order delayed neural networks in a finite-time interval. Numerical example is given to verify the feasibility of the theoretical results.

Transient behavior of coverage processes by applications to the infinite-server queue

1993 ◽  
Vol 30 (3) ◽  
pp. 589-601 ◽  
Author(s):  
Sid Browne ◽  
J. Michael Steele
Keyword(s):  
Line Segment ◽  
Busy Period ◽  
Queueing System ◽  
Transient Behavior ◽  
Infinite Server ◽  
Coverage Process ◽  
Server Queue

We obtain the distribution of the length of a clump in a coverage process where the first line segment of a clump has a distribution that differs from the remaining segments of the clump. This result allows us to provide the distribution of the busy period in an M/G/∞ queueing system with exceptional first service, and applications are considered. The result also provides the tool necessary to analyze the transient behavior of an ordinary coverage process, namely the depletion time of the ordinary M/G/∞ system.

scholarly journals Concavity of the throughput of tandem queueing systems with finite buffer storage space

1990 ◽  
Vol 22 (03) ◽  
pp. 764-767 ◽  
Author(s):  
Ludolf E. Meester ◽  
J. George Shanthikumar
Keyword(s):  
Queueing System ◽  
Queueing Systems ◽  
Sample Path ◽  
Concave Function ◽  
Time Interval ◽  
Single Server ◽  
Finite Buffer ◽  
Buffer Storage ◽  
Unlimited Supply ◽  
Number Of Customers

We consider a tandem queueing system with m stages and finite intermediate buffer storage spaces. Each stage has a single server and the service times are independent and exponentially distributed. There is an unlimited supply of customers in front of the first stage. For this system we show that the number of customers departing from each of the m stages during the time interval [0, t] for any t ≧ 0 is strongly stochastically increasing and concave in the buffer storage capacities. Consequently the throughput of this tandem queueing system is an increasing and concave function of the buffer storage capacities. We establish this result using a sample path recursion for the departure processes from the m stages of the tandem queueing system, that may be of independent interest. The concavity of the throughput is used along with the reversibility property of tandem queues to obtain the optimal buffer space allocation that maximizes the throughput for a three-stage tandem queue.

A queueing system with Markov-dependent arrivals

1985 ◽  
Vol 22 (03) ◽  
pp. 668-677 ◽  
Author(s):  
Pyke Tin
Keyword(s):  
Special Reference ◽  
Correlation Coefficient ◽  
Waiting Time ◽  
Serial Correlation ◽  
Queueing System ◽  
Arrival Process ◽  
Single Server ◽  
Queue Size ◽  
Interarrival Times ◽  
Serial Correlation Coefficient

This paper considers a single-server queueing system with Markov-dependent interarrival times, with special reference to the serial correlation coefficient of the arrival process. The queue size and waiting-time processes are investigated. Both transient and limiting results are given.

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