Mathematics of Operations Research
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Fluid Limits for Processor-Sharing Queues with Impatience We investigate a processor-sharing queue with renewal arrivals and generally distributed service times. Impatient jobs may abandon the queue or renege before completing service. The random time representing a job's patience has a general distribution and may be dependent on its initial service time requirement. A scaling procedure that gives rise to a fluid model with nontrivial yet tract... ... hiện toàn bộ
Mathematics of Operations Research - Tập 33 Số 2 - Trang 375-402 - 2008
Reneging Phenomena in Single Channel Queues We consider a GI/G/1 queueing system where the nth arrival may renege if his service does not commence before an elapsed random time Zn . Results for the general case include relations analogous to Little's formula L = λW, an expression for the average fraction of customers who renege from the system, expressions for the waiting time distribution for all arrivals to th... ... hiện toàn bộ
Mathematics of Operations Research - Tập 4 Số 2 - Trang 162-178 - 1979
Customer Abandonment in Many-Server Queues We study G/G/n + GI queues in which customer patience times are independent, identically distributed following a general distribution. When a customer's waiting time in queue exceeds his patience time, the customer abandons the system without service. For the performance of such a system, we focus on the abandonment process and the queue length process. We prove that under some conditions... ... hiện toàn bộ
Mathematics of Operations Research - Tập 35 Số 2 - Trang 347-362 - 2010
Approximating the GI/GI/1+GI Queue with a Nonlinear Drift Diffusion: Hazard Rate Scaling in Heavy TrafficWe study a single-server queue, operating under the first-in-first-out (FIFO) service discipline, in which each customer independently abandons the queue if his service has not begun within a generally distributed amount of time. Under some mild conditions on the abandonment distribution, we identify a limiting heavy-traffic regime in which the resulting diffusion approximation for both th... ... hiện toàn bộ
Mathematics of Operations Research - Tập 33 Số 3 - Trang 606-644 - 2008
The Functional Equations of Undiscounted Markov Renewal Programming This paper investigates the solutions to the functional equations that arise inter alia in Undiscounted Markov Renewal Programming. We show that the solution set is a connected, though possibily nonconvex set whose members are unique up to n* constants, characterize n* and show that some of these n* degrees of freedom are locally rather than globally independent. Our res... ... hiện toàn bộ
Mathematics of Operations Research - Tập 3 Số 4 - Trang 308-321 - 1978
Generalized Poincaré-Hopf Theorem for Compact Nonsmooth Regions This paper presents an extension of the Poincaré-Hopf theorem to generalized critical points of a function on a compact region with nonsmooth boundary, M, defined by a finite number of smooth inequality constraints. Given a function F: M ↦ ℝn , we define the generalized critical points of F over M, define the index for the critical point, and show that the sum of the i... ... hiện toàn bộ
Mathematics of Operations Research - Tập 32 Số 1 - Trang 193-214 - 2007
Tight Bounds for Permutation Flow Shop Scheduling In flow shop scheduling there are m machines and n jobs, such that every job has to be processed on the machines in the fixed order 1,…,m. In the permutation flow shop problem, it is also required that each machine process the set of all jobs in the same order. Formally, given n jobs along with their processing times on each machine, the goal is to compute a single permutation of the jobs... ... hiện toàn bộ
Mathematics of Operations Research - Tập 34 Số 2 - Trang 417-427 - 2009
Lower and Upper Bounds for the Allocation Problem and Other Nonlinear Optimization Problems We demonstrate the impossibility of strongly polynomial algorithms for the allocation problem, in the comparison model and in the algebraic tree computation model, that follow from lower bound results. Consequently, there are no strongly polynomial algorithms for nonlinear (concave) separable optimization over a totally unimodular constraint matrix. This is in contrast to the case when th... ... hiện toàn bộ
Mathematics of Operations Research - Tập 19 Số 2 - Trang 390-409 - 1994
Measuring the Quality of Approximate Solutions to Zero-One Programming Problems We point out the difficulties associated with measuring the quality of an approximate (heuristic) solution by “Percentage-Error” as is customary. We define a set of properties that are to be expected from a proper measure of solution quality and investigate the family of functions which satisfy those conditions. In particular, we show that for any class of 0–1 programming problems appropr... ... hiện toàn bộ
Mathematics of Operations Research - Tập 6 Số 3 - Trang 319-332 - 1981
On a Class of Totally Unimodular Matrices We examine the class of totally unimodular matrices-that contain no odd cycles, which we call restricted totally unimodular (RTUM). We show that a matrix is RTUM if and only if it can be decomposed in a very simple way into the incidence matrices (or their transposes) of bipartite graphs or directed graphs, and give a linear time algorithm to perform this task. Based on this decomposition... ... hiện toàn bộ
Mathematics of Operations Research - Tập 10 Số 2 - Trang 280-304 - 1985
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