A model for setting services on auxiliary bus lines under congestion

In this paper, a mathematical programming model and a heuristically derived solution is described to assist with the efficient planning of services for a set of auxiliary bus lines (a bus-bridging system) during disruptions of metro and rapid transit lines. The model can be considered static and takes into account the average flows of passengers over a given period of time (i.e., the peak morning traffic hour). Auxiliary bus services must accommodate very high demand levels, and the model presented is able to take into account the operation of a bus-bridging system under congested conditions. A general analysis of the congestion in public transportation lines is presented, and the results are applied to the design of a bus-bridging system. A nonlinear integer mathematical programming model and a suitable approximation of this model are then formulated. This approximated model can be solved by a heuristic procedure that has been shown to be computationally viable. The output of the model is as follows: (a) the number of bus units to assign to each of the candidate lines of the bus-bridging system; (b) the routes to be followed by users passengers of each of the origin–destination pairs; (c) the operational conditions of the components of the bus-bridging system, including the passenger load of each of the line segments, the degree of saturation of the bus stops relative to their bus input flows, the bus service times at bus stops and the passenger waiting times at bus stops. The model is able to take into account bounds with regard to the maximum number of passengers waiting at bus stops and the space available at bus stops for the queueing of bus units. This paper demonstrates the applicability of the model with two realistic test cases: a railway corridor in Madrid and a metro line in Barcelona.     

城市公共交通拥堵的经济分析与计量

基于公共品视角,分析城市交通产品供求特性以及造成拥堵的成因,构建了三部门动态一般均衡模型,分析交通产品供求稳态与冲击对拥堵的影响和动态调控机制,并从产业供求角度提出治理意见.根据动态均衡条件,并以上海城市交通样本构建动态联立方程,进行了实证检验.     

A comparison of shadow prices and reimbursement rates of hospital services

The purpose of this paper is to calculate shadow prices of hospital services and compare them to the reimbursement rates those hospitals receive. These shadow prices are calculated by estimating a multiple-output distance function and applying a dual Shephard's lemma, a technique suggested by Färe and Grosskopf [8]. In contrast to cost functions, distance functions require no price data and do not presume cost minimization. We apply this technique to a sample of California hospitals operating in 1986. We find that hospitals engaged in selective contracting for Medi-Cal patients exhibit closer agreement between relative shadow prices and relative reimbursement rates (Medi-Cal relative to private patients) than noncontracting hospitals.Contact author.     

A convergence analysis of the price of anarchy in atomic congestion games

Mathematical Programming - We analyze the convergence of the price of anarchy (PoA) of Nash equilibria in atomic congestion games with growing total demand T. When the cost functions are...     

Simulation modelling for contracting hospital emergency services at the regional level

Hospital emergency services are closely connected to demographic issues and population changes. The methodology presented here helps to assess the effects of the forecasted demand changes on the next-year emergency unit workloads. The objective of the study is to estimate the expected volume of emergency hospital services, as measured by the number and costs of medical procedures provided to patients, to be contracted by the Polish National Health Fund (NFZ) branch at the regional level to cover the forecasted demand. A discrete-event simulation model was developed to elaborate the credible forecasts of the function components, the fundamental elements of the contract values granted by the NFZ for emergency departments for the following year. Emergency department-level data were drawn from the NFZ regional branch registry to perform a statistical analysis of emergency services provided to patients in 17 admission units and emergency wards in 2010. The model results indicate that the predicted increase in two age groups, i.e., the youngest children and the older population, will have different effects on the number and value of hospital emergency services to be considered in the contracting policy. There is potential for a discrete-event simulation to support strategic health policy decision making at the regional level. The value of this approach lies in providing estimates for the what-if scenarios related to the prognosis of changing acute demand.     

Hopf bifurcation analysis for congestion control with heterogeneous delays

In this paper, a congestion control algorithm with heterogeneous delays is considered. Local stability of the equilibrium solution of this algorithm is investigated based on analyzing the corresponding transcendental characteristic equation. Especially, using one of the system parameters of congestion control algorithm as the bifurcation parameter, when the system parameter exceeds a critical value, the congestion control algorithm undergoes a supercritical Hopf bifurcation, and the explicit formulae determining the stability and the direction of periodic solutions bifurcating from the equilibrium are obtained by applying Hassard et al.’s approaches. Finally, some numerical simulations are performed to verify the theoretical results.     

A modified coupled map car following model and its traffic congestion analysis

Based on the coupled map car following model which was presented by Konishi et al. [Konishi KJ, Kokame H, Hirate K. Phys Rev E 1999;60:4000-7.] (for short, KKH), a modified coupled map car following model is proposed. In this model two successive vehicles’ headway distances in front of the considered one are incorporated in the optimal velocity (for short, OV) function. The stability condition is given for the change of the speed of the preceding vehicle on the base of the control theory. The control scheme in KKH model is applied to the modified model and the feedback gains are determined. Comparison between the modified model and KKH model is carried out. And the corresponding numerical simulation results show that the temporal behavior obtained by our model is better than that by KKH model. The simulation results are in good agreement with the theoretical analysis.     

Measurement and sources of overall and input inefficiencies: Evidences and implications in hospital services

Traditional data envelopment analysis (DEA) focuses exclusively on measuring the overall efficiency of a decision making unit (DMU). Yet, variables that have explanatory power for the overall operational inefficiency of a DMU may not necessarily be the same as those that affect its individual input inefficiencies. On many occasions, variables that explain the overall inefficiency of a DMU can be inconsistent or incongruent with those that cause its individual input inefficiencies. Therefore, we conjecture that an overall inefficiency score alone may have limited value for decision making since such a process requires fine-tuning and adjustments of specific input factors of the DMU in order to maximize its overall efficiency. In this paper, the utilization and financial data of a set of hospitals in California is used to empirically test the above conjecture.Our study has several important contributions and practical implications. First, we fine-tune previous efficiency measures on hospitals by refining input and output measures. Second, with variables on organization, management, demographics, and market competition, we identify specific factors associated with a hospital's overall operational inefficiency. More importantly, by decomposing the overall DEA operational inefficiency score into different individual input inefficiencies (including slacks), we further identify specific variables that cause individual input inefficiency. Third, significant differences are observed among factors of the overall inefficiency and individual input inefficiencies. These findings have important implications for identifying congruent factors for performance standard setting and evaluation; it also provides invaluable information for guiding effective resource allocation and better decision making for improving hospital operational efficiency.     

Stability and Hopf bifurcation analysis in a novel congestion control model with communication delay

In this paper, we investigated Hopf bifurcation by analyzing the distributed ranges of eigenvalues of characteristic linearized equation. Using communication delay as the bifurcation parameter, linear stability criteria dependent on communication delay have also been derived, and, furthermore, the direction of Hopf bifurcation as well as stability of periodic solution for the exponential RED algorithm with communication delay is studied. We find that the Hopf bifurcation occurs when the communication delay passes a sequence of critical values. The stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Finally, a numerical simulation is presented to verify the theoretical results.     

Hopf bifurcation analysis in a fluid flow model of Internet congestion control algorithm

This paper focuses on the Hopf bifurcation analysis of some classes of nonlinear time-delay models, namely fluid flow models, for the Internet congestion control algorithm of TCP/AQM networks. Using tools from control and bifurcation theory, it is proved that there exists a critical value of communication delay for the stability of the network. When the delay passes through the critical value, the system loses its stability and a Hopf bifurcation occurs. Furthermore, the stability of the bifurcation and direction of the bifurcating periodic solutions are determined by applying the normal form theory and the center manifold theorem. Finally, some numerical examples are given to verify the theoretical analysis.     

Calculating the capacity and congestion level of a circular highway

The capacity and congestion level of a circular highway are determined via the discretization of a hydrodynamic model of traffic flows. The relationship between these concepts and their relation to the problem of optimizing the total travel time is demonstrated.     

Transient analysis of a Markovian loss system with heterogeneous inputs for time congestion measurement

This paper presents transient analyses for a Markovian loss system with heterogeneous inputs. Results are applied to the analysis of the measured time congestion of this system. Transient analyses show the properties of system recovery and covariance functions. The measured time congestion is analyzed and approximations are proposed using these properties. These results are significant for management and control in the Integrated Services Digital Network.     

On tree congestion of graphs

This paper investigates the problem of embedding a graph into a tree with the same vertex set (a spanning tree in particular), such that the maximum congestion of the edges is minimized. We calculate exact formulas for the tree congestion and spanning tree congestion for various families of graphs, including grids and complete bipartite graphs.     

A branch and bound based heuristic for makespan minimization of washing operations in hospital sterilization services

In this paper, we address the problem of parallel batching of jobs on identical machines to minimize makespan. The problem is motivated from the washing step of hospital sterilization services where jobs have different sizes, different release dates and equal processing times. Machines can process more than one job at the same time as long as the total size of jobs in a batch does not exceed the machine capacity. We present a branch and bound based heuristic method and compare it to a linear model and two other heuristics from the literature. Computational experiments show that our method can find high quality solutions within short computation time.     

Hopf bifurcation analysis on an Internet congestion control system of arbitrary dimension with communication delay

This paper carries out a Hopf bifurcation analysis on a model of Internet congestion control system for a network with arbitrary topology. The general form of the rate-based Kelly model for a multi-source multi-link network with a communication delay is considered. Assuming the communication delay as a bifurcation parameter, we find that when the delay parameter passes a critical value, a periodic solution bifurcates from the equilibrium point. The stability and direction of bifurcating periodic solutions are studied by using the center manifold theorem and the normal form theory. We simulate our model for a typical example to show the applicability of the approach.