A computer and communications network performance analysis primer
A computer and communications network performance analysis primer
Fundamentals of queueing theory (2nd ed.).
Fundamentals of queueing theory (2nd ed.).
Markovian functionals in teletraffic analysis
Proc. of the international seminar on Teletraffic analysis and computer performance evaluation
Systems Analysis Modelling Simulation
Traffic processes in queueing networks: a Markov renewal approach
Traffic processes in queueing networks: a Markov renewal approach
Processor-sharing queues: some progress in analysis
Queueing Systems: Theory and Applications
Introduction to queueing theory (2nd ed)
Introduction to queueing theory (2nd ed)
On inference concerning time-dependent queue performance: the M/G/1 example
Queueing Systems: Theory and Applications
The average virtual waiting time as a measure of performance
Queueing Systems: Theory and Applications
Time-dependent analysis of M/G/1 vacation models with exhaustive service
Queueing Systems: Theory and Applications
The Fourier-series method for inverting transforms of probability distributions
Queueing Systems: Theory and Applications - Numerical computations in queues
Modelling extremal events: for insurance and finance
Modelling extremal events: for insurance and finance
A personal view of queueing theory
Frontiers in queueing
Probabilistic modelling
Analysis and modeling of World Wide Web traffic for capacity dimensioning of Internet access lines
Performance Evaluation - Special issue on performance and control of network systems
Time-shared Systems: a theoretical treatment
Journal of the ACM (JACM)
Waiting Time Distributions for Processor-Sharing Systems
Journal of the ACM (JACM)
Sharing a Processor Among Many Job Classes
Journal of the ACM (JACM)
A Survey of Analytical Time-Sharing Models
ACM Computing Surveys (CSUR)
An Ergodicity Condition for a Cyclic Queuing System
Cybernetics and Systems Analysis
Fluid approximations for a processor-sharing queue
Queueing Systems: Theory and Applications
Appendix: A primer on heavy-tailed distributions
Queueing Systems: Theory and Applications
Sojourn times in a processor sharing queue with service interruptions
Queueing Systems: Theory and Applications
Sojourn time asymptotics in the M/G/1 processor sharing queue
Queueing Systems: Theory and Applications
Analysis of the M/M/1 Queue with Processor Sharing via Spectral Theory
Queueing Systems: Theory and Applications
Heavy Tails: The Effect of the Service Discipline
TOOLS '02 Proceedings of the 12th International Conference on Computer Performance Evaluation, Modelling Techniques and Tools
The M/G/1 Processor-Sharing Queue with Bulk Arrivals
Proceedings of the IFIP TC6 Task Group/WG6.4 International Workshop on Performance of Communication Systems: Modelling and Performance Evaluation of ATM Technology
Analysis, Design, and Control of Queueing Systems
Operations Research
Answers to Queries to Internet: An Optimal Generation Strategy
Automation and Remote Control
Large Deviation Analysis of Subexponential Waiting Times in a Processor-Sharing Queue
Mathematics of Operations Research
Large Deviations of Square Root Insensitive Random Sums
Mathematics of Operations Research
A MAPK/GK/1/∞ Queueing System with Generalized Foreground-Background Processor Sharing Discipline
Automation and Remote Control
Sojourn time distribution in the M/M/1 queue with discriminatory processor-sharing
Performance Evaluation
Classifying scheduling policies with respect to higher moments of conditional response time
SIGMETRICS '05 Proceedings of the 2005 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Sojourn Times in the M/PH/1 Processor Sharing Queue
Queueing Systems: Theory and Applications
Theory, Volume 1, Queueing Systems
Theory, Volume 1, Queueing Systems
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Numerical Transform Inversion Using Gaussian Quadrature
Probability in the Engineering and Informational Sciences
A sample path relation for the sojourn times in G/G/1-PS systems and its applications
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
A survey on discriminatory processor sharing
Queueing Systems: Theory and Applications
Sojourn Time Tails In The M/D/1 Processor Sharing Queue
Probability in the Engineering and Informational Sciences
On the Laplace transform of the Pareto distribution
Queueing Systems: Theory and Applications
The processor-sharing queue with bulk arrivals and phase-type services
Performance Evaluation
Minimizing the Worst Slowdown: Offline, Online
Operations Research
Queueing networks with discrete time scale: explicit expressions for the steady state behavior of discrete time stochastic networks
Explicit formulas for the variance of conditioned sojourn times in M/D/1-PS
Operations Research Letters
Sojourn time distribution in a MAP/M/1 processor-sharing queue
Operations Research Letters
Analysis of the M/G/1 processor-sharing queue with bulk arrivals
Operations Research Letters
On asymptotics of the emptiness probability in the M/GI/1 queue
Automation and Remote Control
Automation and Remote Control
Is fair resource sharing responsible for spreading long delays?
ACM SIGMETRICS Performance Evaluation Review
Optimal robust policies for bandwidth allocation and admission control in wireless networks
Computer Networks: The International Journal of Computer and Telecommunications Networking
On differential equations arising in the theory of processor sharing queues
Automation and Remote Control
Semi-linear Stochastic Difference Equations
Discrete Event Dynamic Systems
Optimal robust policies for bandwidth allocation and admission control in wireless networks
Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools
Population effects in multiclass processor sharing queues
Proceedings of the Fourth International ICST Conference on Performance Evaluation Methodologies and Tools
On busy period and sojourn time distributions in the M/G/1-EPS queue with catastrophes
Automation and Remote Control
On mathematical models of the service networks
Automation and Remote Control
On sojourn times in M/GI systems under state-dependent processor sharing
Queueing Systems: Theory and Applications
Computer Networks: The International Journal of Computer and Telecommunications Networking
Queuing system with processor sharing and limited resources
Automation and Remote Control
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
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During last few decades the Egalitarian Processor Sharing (EPS) has gained a prominent role in applied probability, especially, in queueing theory and its computer applications. While the EPS paradigm emerged in 1967 as an idealization of round-robin (RR) scheduling algorithm in time-sharing computer systems, it has recently capture renewed interest as a powerful concept for modeling WEB servers. This paper summarizes the most important results concerning the exact solutions for the M/GI/1 queue with egalitarian processor sharing. The material is drawn, mainly, from recent authors' papers which are supplemented, in small degree, by other related results. Many of the further results are established under the direct influence of our earlier papers. Our main purpose is to give a survey of state-of-the-art with regard to main achievements of the contemporary theory of the M/GI/1 queueing system with processor sharing. The focus is on the methods and techniques of exact and asymptotic analysis of this queueing system. In contrast to the standard surveys, the abridged proofs (or their ideas) of some key theorems and corollaries are included in the paper. We outline recent developments in exact analysis of the M/GI/1-EPS queue with further emphasis on time-dependent (transient) probability distributions of the main characteristics. In particular, the present paper includes the results on the joint time-dependent distribution of the sojourn time of a job arriving at time t with the service demand (length) u, and of the number of jobs at time t- in the M/GI/1 queue with egalitarian processor sharing, which obtained in form of multiple transforms. We also show how the non-stationary solutions can be used to obtain known and new results which allow to predict the behaviour of the EPS queue and to yield additional insights into its new unexpected properties. We also discuss a number of limit theorems arising under the study of the processor sharing queues.