Passenger grouping with risk levels in an airport security system

This is a follow-up to the recent paper by Lazar Babu et al. [V.L. Lazar Babu, R. Batta, L. Lin, Passenger grouping under constant threat probability in an airport security system, European Journal of Operational Research 168 (2006) 633–644] which investigated the benefit of classifying passengers into different groups, with the idea that the number of checks and the degree of inspection may vary for different groups. A basic assumption in that paper was that the threat probability is constant across all passengers. In this paper, we relax this assumption and consider the case where passenger risk levels are incorporated. We assume that passengers are classified into several risk classes via some passenger prescreening system, for example, Computer-Assisted Passenger Prescreening System II (CAPPS II). We consider the separate grouping of every class of passengers such that the overall false alarm probability is minimized while maintaining the overall false clear probability within specifications set by a security authority. Meanwhile, we consider the staffing needs at each check station. The problem is formulated as a mixed integer linear program. An illustrative example of the model is presented with comparisons to the model in Lazar Babu et al. (2006) using two performance measures: probability of false alarm and total number of screeners needed. Our conclusion is that incorporation of risk levels through passenger grouping strategies leads to a more efficient security check system.     

Ergodic theorems for queuing systems with dependent inter-arrival times

We study a G/GI/1 single-server queuing model with i.i.d. service times that are independent of a stationary process of inter-arrival times. We show that the distribution of the waiting time converges to a stationary law as time tends to infinity provided that inter-arrival times satisfy a Gärtner-Ellis type condition. A convergence rate is given and a law of large numbers established. These results provide tools for the statistical analysis of such systems, transcending the standard case with independent inter-arrival times.     

The use of decomposition techniques for the analysis of open restricted queuing networks

A number of approximation methods for the analysis of restricted queuing networks that have been presented in the literature are applied to three simple networks. The techniques are shown to be quite fragile in that under reasonable and very general conditions they compute throughout rates which exceed theoretically derived upper bounds.     

Selecting batch size in discrete-time two-phase queuing system

This paper discusses the modeling and analysis of a discrete-time two-phase queuing system. Packets arrive at the system according to a Bernoulli process and receive batch service in the first queue and individual service in the second queue. We study the queue length, average waiting time of packets in the first queue and the effect of batch size on the waiting time.     

Interconnections of Markov chains and quasi-reversible queuing networks

A quasi-reversible queue can be associated with certain type of transactions of a Markov chain. It is shown that if Markov chains are coupled in a certain way, then to the resulting chain be associated a queuing network which is itself quasi-reversible and the stationary distribution of the chain takes the product form. The product form for mixed networks is derived from the result for open networks.     

On queuing systems with failures and several types of input flows

In this paper two models of queuing systems with failures and several types of input flows are considered. These models can simulate the functioning of cellular communications networks under various control regimes. For stationary probabilities of service process (including failed ones) the closed form and the effective calculating algorithms are obtained. The results are used to control the input flows in an optimal way. This research was supported by the INTAS (grant 96-0828).     

A queuing approach for inventory planning with batch ordering in multi-echelon supply chains

This paper presents stylized models for conducting performance analysis of the manufacturing supply chain network (SCN) in a stochastic setting for batch ordering. We use queueing models to capture the behavior of SCN. The analysis is clubbed with an inventory optimization model, which can be used for designing inventory policies . In the first case, we model one manufacturer with one warehouse, which supplies to various retailers. We determine the optimal inventory level at the warehouse that minimizes total expected cost of carrying inventory, back order cost associated with serving orders in the backlog queue, and ordering cost. In the second model we impose service level constraint in terms of fill rate (probability an order is filled from stock at warehouse), assuming that customers do not balk from the system. We present several numerical examples to illustrate the model and to illustrate its various features. In the third case, we extend the model to a three-echelon inventory model which explicitly considers the logistics process.     

Approximate analysis of load-dependent generally distributed queuing networks with low service time variability

In this paper, we present an approximate method for solution of load-dependent, closed queuing networks having general service time distributions with low variability. The proposed technique is an extension of Marie’s (1980) method. In the methodology, conditional throughputs are obtained by an iterative procedure. The iterations are repeated until an invalid result is detected or no improvements are found. We demonstrate the performance of the technique with 10 different examples. On average, the solutions have 5% or lower deviations when compared to simulation results.     

Virtual Braids, Virtual Temperley-Lieb Algebra and f-Polynomial

The authors study the properties of virtual Temperley-Lieb algebra and show how the f-polynomial of virtual knot can be derived from a representation of the virtual braid group into the virtual Temperley-Lieb algebra,which is an approach similar to Jones's original construction.     

Approximate decomposition methods for the analysis of multicommodity flow routing in generalized queuing networks

In this study we deal with network routing decisions and approximate performance evaluation approaches for generalized open queuing networks (OQN), in which commodities enter the network, receive service at one or more arcs and then leave the network. Exact performance evaluation has been applied for the analysis of Jackson OQN, where the arrival and service processes of the commodities are assumed to be Poisson. However, the Poisson processes’ hypotheses are not a plausible or acceptable assumption for the analysis of generalized OQN, as their arrival and service processes can be much less variable than Poisson processes, resulting in overestimated system performance measures and inappropriate flow routing solutions. In this paper we merge network routing algorithms and network decomposition methods to solve multicommodity flow problems in generalized OQN. Our focus is on steady-state performance measures as average delays and waiting times in queue. The main contributions are twofold: (i) to highlight that solving the corresponding multicommodity flow problem by representing the generalized OQN as a Jackson OQN may be a poor approximation and may lead to inaccurate estimates of the system performance measures, and (ii) to present a multicommodity flow algorithm based on a routing step and on an approximate decomposition step, which leads to much more accurate solutions. Computational results are presented in order to show the effectiveness of the proposed approach.     

推广的M~x/G(M/G)/1(M/G)可修排队系统(I)── 一些排队指标

考虑M     

An M/G/1-type queuing model with service times depending on queue length

A study is made of an M/G/1-type queuing model in which customers receive one type of service until such time as, at the end of a service, the queue size is found to exceed a given value N, N ≥ 1. Then a second type of service is put into effect and remains in use until the queue size is reduced to a fixed value K, 0 ≤ K ≤ N. Equations are derived for the stationary probabilities both at departure times and at general times. An algorithm is developed that allows the rapid computation of the mean queue length and some important probabilities.     

推广的M~x/G(M/G)/1(M/G)可修排队系统(I)── 一些排队指标

考虑Ｍｘ／Ｇ（Ｍ／Ｇ）／１（Ｍ／Ｇ）可修排队系统,且把该系统推广到休假时间、服务时间、修理时间和延误休假时间都为任意分布（不一定连续）,利用服务员忙期和拉普拉斯交换,我们直接获得队长瞬态分布的Ｌ变换递推式和稳态分布的递推式,以及队长的概率母函数,同时指出了１９９４年史定华文中存在的错误．     

On the waiting time of arriving aircrafts and the capacity of airports with one or two runways

In this paper we examine a model for the landing procedure of aircrafts at an airport. The characteristic feature here is that due to air turbulence the safety distance between two landing aircrafts depends on the types of these two machines. Hence, an efficient routing of the aircraft to two runways may reduce their waiting time.     

A four-input three-stage queuing network approach to model an industrial system

An industrial system is represented as a four-input, three-stage queuing network in this paper. The four-input queuing network receives orders from clients, and the orders are waiting to be served. Each order comprises (i) time of occurrence of the orders, and (ii) quantity of items to be delivered in each order. The objective of this paper is to compute the optimal path which produces the least response time for the delivery of items to the final destination along the three stages of the network. The average number of items that can be delivered with this minimum response time constitute the optimum capacity of the queuing network. After getting serviced by the last node (a queue and its server) in each stage of the queuing network, a decision is made to route the items to the appropriate node in the next stage which can produce the least response time. Performance measures such as average queue lengths, average response times, average waiting times of the jobs in the four-input network are derived and plotted. Closed-form expressions for the equivalent service rate, equivalent average queue lengths, equivalent response and waiting times of a single equivalent queue with a server representing the entire four-input queuing network are also derived and plotted.     

Virtual criterion for generalized Eagon-Northcott complexes

Given any map of finitely generated free modules, Buchsbaum and Eisenbud define a family of generalized Eagon-Northcott complexes associated to it [3]. We give sufficient criterion for these complexes to be virtual resolutions, thus adding to the known examples of virtual resolutions, particularly those not coming from minimal free resolutions.     

Modelling activities at a neurological rehabilitation unit

A queuing model of a specialist neurological rehabilitation unit is studied. The application is to the Neurological Rehabilitation Centre at Rookwood Hospital (Cardiff, UK), the national rehabilitation unit for Wales. Due to high demand this 21-bed inpatient facility is nearly always at maximum occupancy, and with a significant bed-cost per day this makes it a prime candidate for mathematical modelling. Central to this study is the concept that treatment intensity has an effect on patient length of stay. The model is constructed in four stages. First, appropriate patient groups are determined based on a number of patient-related attributes. Second, a purpose-built scheduling program is used to deduce typical levels of treatment to patients of each group. These are then used to estimate the mean length of stay for each patient group. Finally, the queuing model is constructed. This consists of a number of disconnected homogeneous server queuing systems; one for each patient group. A Coxian phase-type distribution is fitted to the length of time from admission until discharge readiness and an exponential distribution models the remainder of time until discharge. Some hypothetical scenarios suggested by senior management are then considered and compared on the grounds of a number of performance measures and cost implications.     

Simulation modelling and analysis of a border security system

Border control is vital to the security of a nation and its citizens. All countries look at measures to improve the security of their borders. But increasing security can bring a substantial financial burden. In this study, we analyze the border security problem of Turkey using a simulation approach. Our main objective is to find more efficient ways of improving border control and security along Turkey’s land borders. To achieve this, we examine the structure of the border security system and its major elements, examine the relationships between performance measures, and assess the effectiveness of security elements on each system performance measure. We also look into the issues of planned changes and additional resources, and we evaluate new alternative system designs. The results of simulation experiments are analyzed by statistical methods.     

A distance friction minimization approach in data envelopment analysis: A comparative study on airport efficiency

This paper aims to present a newly developed distance friction minimization (DFM) method in the context of data envelopment analysis (DEA) in order to generate an appropriate (non-radial) efficiency-improving projection model, for both input reduction and output increase. In this approach, a generalized distance function, based on a Euclidean distance metric in weighted spaces, is proposed to assist a decision making unit (DMU) to improve its performance by an appropriate movement towards the efficiency frontier surface. A suitable form of multidimensional projection function for efficiency improvement is given by a Multiple Objective Quadratic Programming (MOQP) model. The paper describes the various steps involved in a systematic manner.