On spectral properties of finite population processor shared queues

Population effects in multiclass processor sharing queues

Consider a single server queueing system with several classes of customers, each having its own renewal input process and its own general service times distribution. Upon completing service, customers may leave, or reenter the queue, possibly as customers of a different class. The server is operating under the egalitarian or the discriminatory processor sharing discipline. In this paper, we con...

Limited Processor Sharing Queues and Multi-server Queues

Graph Spectral Properties of Deterministic Finite Automata

We prove that a minimal automaton has a minimal adjacency matrix rank and a minimal adjacency matrix nullity using equitable partition (from graph spectra theory) and Nerode partition (from automata theory). This result naturally introduces the notion of matrix rank into a regular language L, the minimal adjacency matrix rank of a deterministic automaton that recognises L. We then define and fo...

Spectral Properties of Finite Quantum Hall Systems ∗

In this note we review spectral properties of magnetic random Schrödinger operators Hω = H0 + Vω + Ul + Ur defined on L 2(R × [ −L2 , L2 ] , dxdy) with periodic boundary conditions along y. Ul and Ur are two confining potentials for x ≤ −L2 and x ≥ L2 respectively and vanish for −L2 ≤ x ≤ L2 . We describe the spectrum in two energy intervals and we classify it according to the quantum mechanica...

Diffusion Limits of Limited Processor Sharing Queues

We consider a processor sharing queue where the number of jobs served at any time is limited to K, with the excess jobs waiting in a buffer. We use random counting measures on the positive axis to model this system. The limit of this measure-valued process is obtained under diffusion scaling and heavy traffic conditions. As a consequence, the limit of the system size process is proved to be a p...