Phd thesis on queuing theory
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Large scale queueing phd thesis on queuing theory Goldberg, David Alan, Ph. Massachusetts Institute of Technology.
Parallel server queues are a family of stochastic models useful in a variety of applications, including service systems and telecommunication networks.
A particular application that has phd thesis on queuing theory considerable attention in recent years is the analysis of call centers. A feature common to these models is the notion of the 'trade-off' between quality and efficiency.
DSpace@MIT: Large scale queueing systems : asymptotics and insights
It is known that if the underlying system parameters scale together according to a certain 'square-root scaling law', then this trade-off can be precisely phd thesis on queuing theory, in which case the queue is phd thesis on queuing theory to be in the Halfin-Whitt regime. A common phd thesis on queuing theory to understanding this trade-off involves restricting one's models to have exponentially distributed call lengths, and restricting one's analysis to the steady-state behavior of the system.
However, these are considered shortcomings of much work in the area. Although several recent works have moved beyond these assumptions, many open questions remain, especially w.
These questions are the primary focus of this thesis. We identify the limiting rate of convergence just click for source steady-state, discover an asymptotic phase transition that occurs w.
The results of the first part of this thesis represent an important step towards understanding how to incorporate transient effects into the analysis of parallel server queues. We first prove that under minor technical conditions, the steady-state number of queuing theory waiting in queue scales like the phd thesis root of the number of servers.
We then establish bounds for the large deviations behavior of this visit web page, partially resolving a conjecture made queuing theory Gamarnik and Momcilovic in [ We also derive bounds for a related process studied by Reed in [91].
We then derive the first qualitative insights into phd thesis on queuing theory steady-state probability that an arriving job must wait for service in the Halfin-Whitt regime, for generally distributed processing times.
We partially characterize the behavior of this probability when a certain excess parameter B approaches either 0 or oo.
We conclude by studying the large deviations of the number of idle servers, proving that this random variable has a Gaussian-like tail. Queuing prove our main results by combining tools from the phd thesis on queuing theory of stochastic comparison [99] with the theory of heavy-traffic approximations []. Theory compare the system of interest to a phd thesis queue, phd thesis on queuing theory which all servers are kept busy at all times by adding artificial arrivals whenever a server would otherwise go idle, phd thesis on queuing theory certain theory can permanently break down.
We then analyze the modified system using heavy-traffic approximations.
Large scale queueing systems : asymptotics and insights
The proven bounds hold for all n, have representations as the suprema of certain natural processes, and may prove useful in a variety of phd thesis on phd thesis on queuing theory theory. The results of the second part phd thesis on queuing theory this thesis enhance our understanding of how parallel server queues behave in heavy traffic, when phd thesis on queuing theory times are generally distributed. Purchase paper copies of MIT theses. All items in DSpace MIT are protected by original copyright, with all rights reserved, unless otherwise indicated.
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