Queues with Lévy input and hysteretic control

We consider a (doubly) reflected Lévy process where the Lévy exponent is controlled by a hysteretic policy consisting of two stages. In each stage there is typically a different service speed, drift parameter, or arrival rate. We determine the steady-state performance, both for systems with finite and infinite capacity. Thereby, we unify and extend many existing results in the literature, focusing on the special cases of M/G/1 queues and Brownian motion. © The Author(s) 2009

ANALYSIS OF BULK ARRIVALS IN QUEUEING MODELS

       Present paper surveys the literature on bulk queueing models. The concept of bulk arrivals and bulk services has gained a tremendous significance in present situations. Due to congestion problem everywhere (banks, metro stations, bus stops, railway reservation, traffic … etc.) researchers have to focus their attention to develop models and mechanism to deal with the same. A number of models have been developed in the area of queueing theory incorporating bulk queueing models. These bulk queueing models can be applied to resolve the congestion problems. Through this survey, an attempt has been made to review the work done on bulk queues, modeling various phenomenons. The goal is to provide sufficient information to analysts, managers and industry people who are interested in using queueing theory to model congestion problems and want to locate the details of relevant models

Multi-threshold Control of the BMAP/SM/1/K Queue with Group Services

We consider a finite capacity queue in which arrivals occur according to a batch Markovian arrival process (BMAP). The customers are served in groups of varying sizes. The services are governed by a controlled semi-Markovian process according to a multithreshold strategy. We perform the steady-state analysis of this model by computing (a) the queue length distributions at departure and arbitrary epochs, (b) the Laplace-Stieltjes transform of the sojourn time distribution of an admitted customer, and (c) some selected system performance measures. An optimization problem of interest is presented and some numerical examples are illustrated

On a make-to-stock production/mountain model with hysteretic control

We consider a make-to-stock production-inventory model with one machine that produces stock in a buffer. The machine is subject to breakdowns. During up periods, the machine fils the buffer at a level-dependent rate a(x) > 0. During down periods, the production rate is zero, and the demand rate is either ß(x) > 0 or ¿(x) > 0 when the inventory level is x; which of the two demand rates applies depends on a hysteretic control policy. We determine the conditions under which the steady-state distribution of the inventory level exists, and we derive that distribution. Other performance measures under consideration are the number of switches from ß(.) to ¿(.) per busy period, the busy period distribution, and the overshoot above a particular hysteretic level

Analytical Approaches to Improve the Defensive Asylum Process at the United States Southern Border

This Major Qualifying Project encompasses an analysis of the United States defensive asylum process with the goal of providing information to assist decision makers for immigration policy. Currently, there are over one million pending immigration cases that include asylum seekers who are waiting for a hearing. Through the use of data and regression analysis, queuing theory, simulation, and optimization, the team developed a web-based tool to aid in resource allocation at the United States southern border. The web tool takes these relationships and user input data to output a sector-by-sector allocation of judicial resources to minimize time in system, queue size, and costs

Queues with delays in two-state strategies and Lévy input

We consider a reflected Lévy process without negative jumps, starting at the origin. When the reflected process first upcrosses level K, a timer is activated. After D time units, the timer expires and the Lévy exponent of the Lévy process is changed. As soon as the process hits zero again, the Lévy exponent reverses to the original function. If the process has reached the origin before the timer expires then the Lévy exponent does not change. Using martingale techniques, we analyze the steady-state distribution of the resulting process, reflected at the origin. We pay special attention to the cases of deterministic and exponential timers, and to the following three special Lévy processes: (i) a compound Poisson process plus negative drift (corresponding to an M/G/1 queue), (ii) Brownian motion, and (iii) a Lévy process that is a subordinator until the timer expires. © Applied Probability Trust 2008