A simple solution for the M/D/c waiting time distribution

Franx, Geert Jan

doi:10.1016/s0167-6377(01)00108-0

Cited by 56 publications

(39 citation statements)

References 2 publications

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“…The limiting result for P(M β = 0) has the appealing property that the time to compute it does not depend on the number of servers, which is the case for standard computational procedures for the M/D/s queue, see e.g. Tijms [32] and Franx [10] and references therein. The main aim of this paper is to obtain series expansions refining this asymptotic result.…”

Section: Goals Results and Insightsmentioning

confidence: 99%

Corrected asymptotics for a multi-server queue in the Halfin-Whitt regime

2008

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To investigate the quality of heavy-traffic approximations for queues with many servers, we consider the steady-state number of waiting customers in an M/D/s queue as s → ∞. In the Halfin-Whitt regime, it is well known that this random variable converges to the supremum of a Gaussian random walk. This paper develops methods that yield more accurate results in terms of series expansions and inequalities for the probability of an empty queue, and the mean and variance of the queue length distribution. This quantifies the relationship between the limiting system and the queue with a small or moderate number of servers. The main idea is to view the M/D/s queue through the prism of the Gaussian random walk: as for the standard Gaussian random walk, we provide scalable series expansions involving terms that include the Riemann zeta function.

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Section: Goals Results and Insightsmentioning

confidence: 99%

Corrected asymptotics for a multi-server queue in the Halfin-Whitt regime

2008

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“…To derive E[W (t)] we evaluate the cumulative distribution of the delay W (t) experienced by a user arriving at time t following the methods proposed in [21], [22]. We generalize the approach considering non-homogeneous arrival rates and an unknown initial state u(T sc ).…”

Section: Delay Analysismentioning

confidence: 99%

Large Scale Control of Deferrable Domestic Loads in Smart Grids

Tinnirello

Neglia

Giarré

et al. 2018

IEEE Trans. Smart Grid

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Abstract-In this paper, we investigate a realistic and lowcost deployment of large scale direct control of inelastic home appliances whose energy demand cannot be shaped, but simply deferred. The idea is to exploit 1) some simple actuators to be placed on the electric plugs for connecting or disconnecting appliances with heterogeneous control interfaces, including nonsmart appliances, and 2) the Internet connections of customers for transporting the activation requests from the actuators to a centralized controller. Our solution requires no interaction with home users: in particular, it does not require them to express their energy demand in advance. A queuing theory model is derived to quantify how many users should adopt this solution in order to control a significant aggregated power load without significantly impairing their quality of service.

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“…Franx [12] showed that the waiting time probability for M/D/n is: The equations can be solved using the fast Fourier transform and a geometric tail approach [13].…”

Section: Performance Of a Sip-based Grid Systemmentioning

confidence: 99%

Towards a light-weight bag-of-tasks grid architecture

Basicevic

Cetic

Popović

et al. 2015

Telfor

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-The paper presents the application of SIP protocol in the context of bag-of-tasks grid architecture. The SIP protocol has been used in the realization of the execution management service. The main idea is the use of stateful SIP proxy as a request broker. The paper provides a description of the concept, and the prototype system that has been built, as well as the calculation of estimated performance level and its relation to maximum RTT of grid system. The main advantage of this light-weight grid architecture is the reuse of a mature infrastructure. A short overview of some approaches to the mathematical modeling of computer grids is included.

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A simple solution for the M/D/c waiting time distribution

Cited by 56 publications

References 2 publications

Corrected asymptotics for a multi-server queue in the Halfin-Whitt regime

Corrected asymptotics for a multi-server queue in the Halfin-Whitt regime

Large Scale Control of Deferrable Domestic Loads in Smart Grids

Towards a light-weight bag-of-tasks grid architecture

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