[Tip: Study the MC, QT, and Little's law lectures together: CTMC (MC lecture), M/M/1 queue (QT lecture), Little's law lecture (when deriving the mean response time from mean number of customers), DTMC (MC lecture), M/M/1 queue derivation using DTMC analysis, derive distribution of response time in M/M/1 queue (QT lecture), relation between Markov property and mem-oryless property (MC lecture), ...

In this paper we study a broad class of semi-Markovian queues introduced by Sengupta. This class contains many classical queues such as the GI/M/1 queue, SM/MAP/1 queue and others, as well as queues with correlated inter-arrival and service times. Queues belonging to this class are characterized by a set of matrices of size m and Sengupta showed that its waiting time distribution can be represe...

Two-phase M/Ek/1 queueing system with N -policy for exhaustive batch service with gating, and server startups and breakdowns is studied in this paper. The customers arrive individually according to a Poisson process and waiting customers receive batch service all at a time in the first phase and are served individually in the second phase. The server is turned off each time the system empties, ...

Consider a single server queue with renewal arrivals and i.i.d. service times in which the server operates under a processor sharing service discipline. To describe the evolution of this system, we use a measure valued process that keeps track of the residual service times of all jobs in the system at any given time. From this measure valued process, one can recover the traditional performance ...

We consider an unreliable multi-server queue in which the rate of servers’ breakdowns increases when the number of broken servers grows. To prevent quick degradation of the system, it is proposed to switch to a quarantine regime when the number of broken servers exceeds some threshold and to maintain this regime until the number of broken servers becomes less than another threshold. During the ...

The universal scalability law (USL) of computational capacity is a rational function Cp = P (p)/Q(p) with P (p) a linear polynomial and Q(p) a second-degree polynomial in the number of physical processors p, that has been long used for statistical modeling and prediction of computer system performance. We prove that Cp is equivalent to the synchronous throughput bound for a machine-repairman wi...

A novel approach for obtaining the response time in a discrete-time tandem-queue with blocking is presented. The approach constructs a Markov chain based on the age of the leading customer in the first queue. We also provide a stability condition and carry out several numerical examples. © 2004 Elsevier B.V. All rights reserved.

Consider a single server queue with renewal arrivals and i.i.d. service times in which the server operates under a processor sharing service discipline. To describe the evolution of this system, we use a measure valued process that keeps track of the residual service times of all jobs in the system at any given time. From this measure valued process, one can recover the traditional performance ...

We consider the optimal servicing of a queue with sigmoid server performance. There are various systems with sigmoid server performance including systems involving human decision making, visual perception, human-machine communication and advertising response. The tasks arrive at the server according to some stochastic process. Each task has a deadline that is incorporated as a latency penalty. ...

 In this paper we develop queuing model results for a single “automated” workstation that receives jobs from another automated workstation. An automated workstation is a server with deterministic processing times that experiences random operating times between failures, and then subsequent random repair times. We develop analytical expressions for the queue size distribution, the average numbe...