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
Reduced-Load Equivalence and Induced Burstiness in GPS Queues with Long-Tailed Traffic Flows
Queueing Systems: Theory and Applications
Performance Evaluation - Performance 2005
Processor sharing: A survey of the mathematical theory
Automation and Remote Control
Waiting times for M/M systems under state-dependent processor sharing
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
Hi-index | 0.00 |
We consider a system with Poisson arrivals and i.i.d. service times. The requests are served according to the state-dependent processor-sharing discipline, where each request receives a service capacity which depends on the actual number of requests in the system. The linear systems of PDEs describing the residual and attained sojourn times coincide for this system, which provides time reversibility including sojourn times for this system, and their minimal non-negative solution gives the LST of the sojourn time V(驴) of a request with required service time 驴. For the case that the service time distribution is exponential in a neighborhood of zero, we derive a linear system of ODEs, whose minimal non-negative solution gives the LST of V(驴), and which yields linear systems of ODEs for the moments of V(驴) in the considered neighborhood of zero. Numerical results are presented for the variance of V(驴). In the case of an M/GI/2-PS system, the LST of V(驴) is given in terms of the solution of a convolution equation in the considered neighborhood of zero. For service times bounded from below, surprisingly simple expressions for the LST and variance of V(驴) in this neighborhood of zero are derived, which yield in particular the LST and variance of V(驴) in M/D/2-PS.