Dynamic Service Rate Control for a Single Server Queue with Markov Modulated Arrivals

We consider the problem of service rate control of a single server queueing system with a finite-state Markov-modulated Poisson arrival process. We show that the optimal service rate is non-decreasing in the number of customers in the system; higher congestion rates warrant higher service rates. On the contrary, however, we show that the optimal service rate is not necessarily monotone in the current arrival rate. If the modulating process satisfies a stochastic monotonicity property the monotonicity is recovered. We examine several heuristics and show where heuristics are reasonable substitutes for the optimal control. None of the heuristics perform well in all the regimes. Secondly, we discuss when the Markov-modulated Poisson process with service rate control can act as a heuristic itself to approximate the control of a system with a periodic non-homogeneous Poisson arrival process. Not only is the current model of interest in the control of Internet or mobile networks with bursty traffic, but it is also useful in providing a tractable alternative for the control of service centers with non-stationary arrival rates.Comment: 32 Pages, 7 Figure

Network revenue management with product-specific no-shows

Revenue management practices often include overbooking capacity to account for customers who make reservations but do not show up. In this paper, we consider the network revenue management problem with no-shows and overbooking, where the show-up probabilities are specific to each product. No-show rates differ significantly by product (for instance, each itinerary and fare combination for an airline) as sale restrictions and the demand characteristics vary by product. However, models that consider no-show rates by each individual product are difficult to handle as the state-space in dynamic programming formulations (or the variable space in approximations) increases significantly. In this paper, we propose a randomized linear program to jointly make the capacity control and overbooking decisions with product-specific no-shows. We establish that our formulation gives an upper bound on the optimal expected total profit and our upper bound is tighter than a deterministic linear programming upper bound that appears in the existing literature. Furthermore, we show that our upper bound is asymptotically tight in a regime where the leg capacities and the expected demand is scaled linearly with the same rate. We also describe how the randomized linear program can be used to obtain a bid price control policy. Computational experiments indicate that our approach is quite fast, able to scale to industrial problems and can provide significant improvements over standard benchmarks.Network revenue management, linear programming, simulation, overbooking, no-shows.

Delayed purchase options in single-leg revenue management

Many airline reservation systems offer the commitment option to their potential passengers. This option allows passengers to reserve a seat for a fixed duration before making a final purchase decision. In this study, we develop single-leg revenue management models that consider such contingent commitment decisions. We start with a dynamic programming model of this problem. This model is computationally intractable as it requires storing a multidimensional state space because of bookkeeping of the committed seats. To alleviate this difficulty, we propose an alternate dynamic programming formulation that uses an approximate model of how the contingent commitments behave and we show how to extract a capacity allocation policy from the approximate dynamic programming formulation. In addition, we present a deterministic linear programming model that gives an upper bound on the optimal expected revenue from the intractable dynamic programming model. As the problem size becomes large in terms of flight capacity and the expected number of arrivals, we demonstrate an asymptotic lower bound for the deterministic linear programming model. Our extensive numerical study indicates that offering commitment options can noticeably increase potential revenue even though offering a contingent commitment option may not always be in the best interest of the airline. Also, our results show that the proposed approximate dynamic programming model coordinates capacity allocation and commitment decisions quite well

Violence as a Vicious Cycle

Since the conclusion that the violence as a behavior is not (cannot be) determined within an absolute genetic determinism has been reached for long years, environmental factors are increasingly examined. We witness that human behavior in society can easily convert into coping with stressful events with violence. Individual or social violence as a behavior has a similar pattern with violence committed in primitive society and by children. After a brief review of violence, its description, etiological theories and types, this article majorly focuses on children and their early and late response to violence. The purpose here is to draw attention to the individuals who were previously exposed to violence (either directly or indirectly) resort to violence, perpetuating a vicious cycle

IDENTIFYING EFFECTIVE POLICIES IN APPROXIMATE DYNAMIC PROGRAMMING: BEYOND REGRESSION

ABSTRACT Dynamic programming formulations may be used to solve for optimal policies in Markov decision processes. Due to computational complexity dynamic programs must often be solved approximately. We consider the case of a tunable approximation architecture used in lieu of computing true value functions. The standard methodology advocates tuning the approximation architecture via sample path information and regression to get a good fit to the true value function. We provide an example which shows that this approach may unnecessarily lead to poorly performing policies and suggest direct search methods to find better performing value function approximations. We illustrate this concept with an application from ambulance redeployment

Volume CXIV, Number 4, November 7, 1996

Objective: Turner syndrome (TS) is a chromosomal disorder caused by complete or partial X chromosome monosomy that manifests various clinical features depending on the karyotype and on the genetic background of affected girls. This study aimed to systematically investigate the key clinical features of TS in relationship to karyotype in a large pediatric Turkish patient population.Methods: Our retrospective study included 842 karyotype-proven TS patients aged 0-18 years who were evaluated in 35 different centers in Turkey in the years 2013-2014.Results: The most common karyotype was 45,X (50.7%), followed by 45,X/46,XX (10.8%), 46,X,i(Xq) (10.1%) and 45,X/46,X,i(Xq) (9.5%). Mean age at diagnosis was 10.2±4.4 years. The most common presenting complaints were short stature and delayed puberty. Among patients diagnosed before age one year, the ratio of karyotype 45,X was significantly higher than that of other karyotype groups. Cardiac defects (bicuspid aortic valve, coarctation of the aorta and aortic stenosis) were the most common congenital anomalies, occurring in 25% of the TS cases. This was followed by urinary system anomalies (horseshoe kidney, double collector duct system and renal rotation) detected in 16.3%. Hashimoto's thyroiditis was found in 11.1% of patients, gastrointestinal abnormalities in 8.9%, ear nose and throat problems in 22.6%, dermatologic problems in 21.8% and osteoporosis in 15.3%. Learning difficulties and/or psychosocial problems were encountered in 39.1%. Insulin resistance and impaired fasting glucose were detected in 3.4% and 2.2%, respectively. Dyslipidemia prevalence was 11.4%.Conclusion: This comprehensive study systematically evaluated the largest group of karyotype-proven TS girls to date. The karyotype distribution, congenital anomaly and comorbidity profile closely parallel that from other countries and support the need for close medical surveillance of these complex patients throughout their lifespa

A tighter variant of Jensen's lower bound for stochastic programs and separable approximations to recourse functions

In this paper, we propose a new method to compute lower bounds on the optimal objective value of a stochastic program and show how this method can be used to construct separable approximations to the recourse functions. We show that our method yields tighter lower bounds than Jensen's lower bound and it requires a reasonable amount of computational effort even for large problems. The fundamental idea behind our method is to relax certain constraints by associating dual multipliers with them. This yields a smaller stochastic program that is easier to solve. We particularly focus on the special case where we relax all but one of the constraints. In this case, the recourse functions of the smaller stochastic program are one dimensional functions. We use these one dimensional recourse functions to construct separable approximations to the original recourse functions. Computational experiments indicate that our lower bounds can significantly improve Jensen's lower bound and our recourse function approximations can provide good solutions.Stochastic programming Lower bounds Recourse function approximation

On the asymptotic optimality of the randomized linear program for network revenue management

For network revenue management problems, it is known that the bid prices computed through the so-called deterministic linear program are asymptotically optimal as the capacities on the flight legs and the expected numbers of product requests increase linearly with the same rate. In this paper, we show that the same asymptotic optimality result holds for the bid prices computed through the so-called randomized linear program. We computationally investigate how the performance of the randomized linear program changes with different problem parameters and with the number of samples. The hope is that our asymptotic optimality result and computational experiments will raise awareness for the randomized linear program, which has yet not been popular in the research community or industry.OR in airlines Revenue management Control