# Insensitive bounds for the moments of the sojourn time distribution in the M/G/1 processor-sharing queue

@article{Cheung2006InsensitiveBF, title={Insensitive bounds for the moments of the sojourn time distribution in the M/G/1 processor-sharing queue}, author={Sing-Kong Cheung and Hans van den Berg and Richard J. Boucherie}, journal={Queueing Systems}, year={2006}, volume={53}, pages={7-18} }

This paper studies the M/G/1 processor-sharing (PS) queue, in particular the sojourn time distribution conditioned on the initial job size. Although several expressions for the Laplace-Stieltjes transform (LST) are known, these expressions are not suitable for computational purposes. This paper derives readily applicable insensitive bounds for all moments of the conditional sojourn time distribution. The instantaneous sojourn time, i.e., the sojourn time of an infinitesimally small job, leads…

## 21 Citations

### Insensitive Bounds for the Moments of the Sojourn Times in M/GI Systems Under State-Dependent Processor Sharing

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This work derives expressions as well as tight insensitive upper bounds for the moments of the conditional sojourn time of a request with given required service time for a state-dependent processor-sharing system with Poisson arrivals and independent and identically distributed service times.

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A system where the arrivals form a Poisson process and the required service times of the requests are exponentially distributed is considered, which derives systems of ordinary differential equations for the LST and for the moments of the conditional waiting time of a request with given required service time as well as a stable and fast recursive algorithm for the second moment of the unconditional waiting time.

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It turns out that the sojourn time of some kind of virtual requests equals in distribution an additive functional of a stationary time-changed process, which provides bounds for the expectation of functions of virtualSojourn times, in particular bounds for fractional moments and the distribution function.

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We deal with an infinite-server system where the
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This contribution avoids frequently used transform and inversion problems by a decomposition of the transition state model in the original domain by converting the relevant differential-recurrence backward equation system to a sum of a service component and an arrival–departure component.

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### Simple Near-Optimal Scheduling for the M/G/1

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M-SERPT is presented, a new variant of SERPT which is as simple as SERPT but has provably near-optimal mean response time at all loads for any job size distribution and is the only non-Gittins scheduling policy known to have a constant-factor approximation ratio formean response time.

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This work considers the problem of preemptively scheduling jobs to minimize mean response time of an M/G/1 queue and proposes the shortest expected remaining processing time (SERPT) policy, a natural extension of SRPT to unknown job sizes.

### Simple Near-Optimal Scheduling for the M/G/1

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The problem of preemptively scheduling jobs to minimize mean response time of an M/G/1 queue is considered and the shortest expected remaining processing time (SERPT) policy is considered.

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