Analysis of Performability for Stochastic Models of Fault-Tolerant Systems
IEEE Transactions on Computers
Processor-sharing queues: some progress in analysis
Queueing Systems: Theory and Applications
The M/G/1 queue with processor sharing and its relation to a feedback queue
Queueing Systems: Theory and Applications
Time-shared Systems: a theoretical treatment
Journal of the ACM (JACM)
Waiting Time Distributions for Processor-Sharing Systems
Journal of the ACM (JACM)
Insensitivity in processor-sharing networks
Performance Evaluation
On Stochastic Bounds for Monotonic Processor Sharing Networks
Queueing Systems: Theory and Applications
A survey on statistical bandwidth sharing
Computer Networks: The International Journal of Computer and Telecommunications Networking - Special issue: In memroy of Olga Casals
Performance Evaluation - Performance 2005
Large deviations of sojourn times in processor sharing queues
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
Sojourn time asymptotics in processor-sharing queues
Queueing Systems: Theory and Applications
Sojourn Time Tails In The M/D/1 Processor Sharing Queue
Probability in the Engineering and Informational Sciences
ACM SIGMETRICS Performance Evaluation Review
Sojourn time asymptotics in Processor Sharing queues with varying service rate
Queueing Systems: Theory and Applications
On modelling the performance and reliability of multimode computer systems
Journal of Systems and Software
The equivalence between processor sharing and service in random order
Operations Research Letters
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The paper addresses multiclass processor sharing systems with general state-dependent service rates, exponential service requirements and a finite service pool. By considering the amount of service received by a permanent customer and associating this service with the evolution of a Markov Reward process, the sojourn time distribution is formulated in terms of a matrix exponential expression. When the service rates are balanced, this expression can be diagonalized. Tail asymptotics are also discussed. The matrix exponential expression is subsequently exploited towards the study of time scale separation regimes. Unlike the standard practice of assuming a distinct time scale per class, the paper groups more realistically all customer classes in two time scales. Provably tight approximations, of a known, small degree of error, are developed for the sojourn time distribution of a given class (with either fast or slow dynamics), in terms of reduced models containing only the customer classes operating in the same time scale. The approximation for the fast classes gives rise to further characterization of the tail behavior. Additionally, the paper studies another, more specialized variant of the time scale separation regime, in which the service rates take a special form that leads to even simpler approximations. Finally, it is shown that the essence of the main results applies also to the more general setting of service requirement distributions with Markovian phase-type form.