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

  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},
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… 

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

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.

Waiting times for M/M systems under state-dependent processor sharing

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.

Additive functionals with application to sojourn times in infinite-server and processor sharing systems

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.

On sojourn times for an infinite-server system in random environment and its application to processor sharing systems

We deal with an infinite-server system where the service speed is governed by a stationary and ergodic process with countably many states. Applying a random time transformation such that the

Communication Networks The uniform estimation of the M/G/1 processor sharing response time distribution

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.

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

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.

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

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

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.



Sojourn time asymptotics in the M/G/1 processor sharing queue

It is shown that the M/G/1 processor sharing queue that the service time distribution is regularly varying of index -ν, ν non-integer, iff the sojourn time distribution was previously shown to be regularly varying, and a new expression for the Laplace–Stieltjes transform of theSojournTime distribution is derived.

The sojourn-time distribution in the M/G/1 queue by processor sharing

  • T. Ott
  • Mathematics
    Journal of Applied Probability
  • 1984
This paper gives, in the form of Laplace–Stieltjes transforms and generating functions, the joint distribution of the sojourn time and the number of customers in the system at departure for customers

The M/G/1 processor-sharing model: transient behavior

  • M. Kitaev
  • Mathematics
    Queueing Syst. Theory Appl.
  • 1993
This paper deals with the M/G/1 model with processor-sharing service discipline and shows that for initial conditions of special kind (there is one job or none) the results can be expressed in a closed form.


In this paper, the classical M/G/1 processor-sharing queue is studied under the assumption that there tend to be some jobs much longer than others, as occurs with a heavy-tailed service-requirement distribution, and the evolution of the long and short jobs in diierent time scales is suggested.

Predicting Response Times in Processor-Sharing Queues

This work investigates the possibility of reliably predicting response times in real time in the M/G/1 processor-sharing queue by proving laws of large numbers and central limit theorem refinements and calculating the conditional mean and variance of the response time, given the state information, by numerically inverting Laplace transforms.

TheM/G/1 queue with processor sharing and its relation to a feedback queue

The central model of this paper is anM/M/1 queue with a general probabilistic feedback mechanism, where the mean service time at each loop shrink to zero and the feedback probabilities approach one in such a way that the mean total required service time remains constant.


In many modern computer-communication systems, a job may be processed in several phases, or a job may generate new tasks. Such phenomena can be modeled by service systems with feedback. In the

On a relationship between processor-sharing queues and Crump–Mode–Jagers branching processes

The M/G/1 queue with batch arrivals and a queueing discipline which is a generalization of processor sharing is studied by means of Crump–Mode–Jagers branching processes. A number of theorems are

Processor-sharing queues: Some progress in analysis

This paper reviews some recent results based on new techniques used in the analysis of main processor-sharing queueing systems. These results include the solutions of the problems of determining the