Linear loss networks

This paper investigates theoretical properties of throughput and cost in linear loss networks. The maximum throughput of the network with exponential service times is derived and the arrival process that maximizes throughput, given a fixed arrival rate, is established. For general service times, an asymptotically critical loading regime is identified such that the probability of an arbitrary customer being lost is strictly within (0,1) as the network size increases. This regime delivers throughput comparable to the maximum at a relatively low network cost. The paper establishes the asymptotic throughput and network cost under this critical loading.     

Fast simulation of blocking probabilities in loss networks

This paper is concerned with the determination of blocking probabilities in loss networks. In fact, our study consists of two parts. Primarily, we scale both arrival rates and link capacities, in order to derive rough asymptotical expressions. These expressions arise as the result of mathematical programming problems. Secondly, we develop a fast simulation technique to estimate the blocking probabilities. This technique is based on importance sampling, where the choice of the alternative probability model is closely related to the optimizing arguments of the above mentioned mathematical programming problem. Some examples show that huge gain of simulation effort can be achieved.     

Asymptotic marginal independence in large networks of loss systems

Network models in which each node is a loss system frequently arise in telephony. Models with several hundred nodes are common. Suppose a customer requires a server from each of several nodes. It would be convenient if the probability that the required servers are all free were approximately a product, where each term is the probability a required node has a free server. We present some theorems to support this approximation. Most of the theorems are restricted to nodes with one server. Some of the difficulties in analyzing nodes with multiple servers are described.     

Non-cooperative competition among revenue maximizing service providers with demand learning

This paper recognizes that in many decision environments in which revenue optimization is attempted, an actual demand curve and its parameters are generally unobservable. Herein, we describe the dynamics of demand as a continuous time differential equation based on an evolutionary game theory perspective. We then observe realized sales data to obtain estimates of parameters that govern the evolution of demand; these are refined on a discrete time scale. The resulting model takes the form of a differential variational inequality. We present an algorithm based on a gap function for the differential variational inequality and report its numerical performance for an example revenue optimization problem.     

Nonstationary analysis of the loss queue and of queueing networks of loss queues

We present an iterative scheme based on the fixed-point approximation method, for the numerical calculation of the time-dependent mean number of customers and blocking probability functions in a nonstationary queueing network with multi-rate loss queues. We first show how the proposed method can be used to analyze a single-class, multi-class, and multi-rate nonstationary loss queue. Subsequently, the proposed method is extended to the analysis of a nonstationary queueing network of multi-rate loss queues. Comparisons with exact and simulation results showed that the results are consistently close to the exact results and they are always within simulation confidence intervals.     

A knowledge based approach to loss severity assessment in financial institutions using Bayesian networks and loss determinants

Modelling loss severity from rare operational risk events with potentially catastrophic consequences has proved a difficult task for practitioners in the finance industry. Efforts to develop loss severity models that comply with the BASEL II Capital Accord have resulted in two principal model directions where one is based on scenario generated data and the other on scaling of pooled external data. However, lack of relevant historical data and difficulties in constructing relevant scenarios frequently raise questions regarding the credibility of the resulting loss predictions. In this paper we suggest a knowledge based approach for establishing severity distributions based on loss determinants and their causal influence. Loss determinants are key elements affecting the actual size of potential losses, e.g. market volatility, exposure and equity capital. The loss severity distribution is conditional on the state of the identified loss determinants, thus linking loss severity to underlying causal drivers. We suggest Bayesian Networks as a powerful framework for quantitative analysis of the causal mechanisms determining loss severity. Leaning on available data and expert knowledge, the approach presented in this paper provides improved credibility of the loss predictions without being dependent on extensive data volumes.     

Competition among parties and power: an empirical analysis

This study develops a bi-objective method for burn-in decision makings with a view to achieving an optimal trade-off between the cost and the performance measures. Under the proposed method, a manufacturer specifies the relative importance between the cost and the performance measures. Then a single-objective optimal solution can be obtained through optimizing the weighted combination of these two measures. Based on this method, we build a specific model when the performance objective is the survival probability given a mission time. We prove that the optimal burn-in duration is decreasing in the weight assigned to the normalized cost. Then, we develop an algorithm to populate the Pareto frontier in case the manufacturer has no idea about the relative weight.     

Monotonicity and error bounds for networks of Erlang loss queues

Networks of Erlang loss queues naturally arise when modelling finite communication systems without delays, among which, most notably are

1. classical circuit switch telephone networks (loss networks) and
2. present-day wireless mobile networks.

Performance measures of interest such as loss probabilities or throughputs can be obtained from the steady state distribution. However, while this steady state distribution has a closed product form expression in the first case (loss networks), it does not have one in the second case due to blocked (and lost) handovers. Product form approximations are therefore suggested. These approximations are obtained by a combined modification of both the state space (by a hypercubic expansion) and the transition rates (by extra redial rates). It will be shown that these product form approximations lead to

• upper bounds for loss probabilities and
• analytic error bounds for the accuracy of the approximation for various performance measures.

The proofs of these results rely upon both monotonicity results and an analytic error bound method as based on Markov reward theory. This combination and its technicalities are of interest by themselves. The technical conditions are worked out and verified for two specific applications:

• pure loss networks as under (i)
• GSM networks with fixed channel allocation as under (ii).

The results are of practical interest for computational simplifications and, particularly, to guarantee that blocking probabilities do not exceed a given threshold such as for network dimensioning.     

Approximate analysis of non-stationary loss queues and networks of loss queues with general service time distributions

A Fixed Point Approximation (FPA) method has recently been suggested for non-stationary analysis of loss queues and networks of loss queues with Exponential service times. Deriving exact equations relating time-dependent mean numbers of busy servers to blocking probabilities, we generalize the FPA method to loss systems with general service time distributions. These equations are combined with associated formulae for stationary analysis of loss systems in steady state through a carried load to offered load transformation. The accuracy and speed of the generalized methods are illustrated through a wide set of examples.     

On equilibrium analysis of acyclic multiclass loss networks under admission control

We consider equilibrium analysis of several dynamic resource sharing policies for multiclass loss networks with acyclic topologies. The policies of interest are based on the principle of prioritizing classes via thresholding or reservation. We show that under each policy the equilibrium network state is a Markov random field and we obtain closed form expressions for the conditional probabilities therein. Such representations drastically reduce the computational complexity of blocking probability and revenue calculations. We provide revenue comparison of the considered policies and several extensions of the applied analytical technique.     

Competition among non-life insurers under solvency constraints: A game-theoretic approach

We formulate a noncooperative game to model competition for policyholders among non-life insurance companies, taking into account market premium, solvency level, market share and underwriting results. We study Nash equilibria and Stackelberg equilibria for the premium levels, and give numerical illustrations.     

Payment models to coordinate healthcare providers: Extension to risk-averse providers

Previous works compared the performance of the bundled and unbundled payment schemes in a referral-based setting where the providers (generalist and specialist) are risk-neutral and health outcomes are partial attributable to the providers. In this work, we extend the results to a setting where the providers are risk-averse. We also show that a bundled scheme has higher referral rates, lower time spent by the specialist, higher specialist utilization relative to an unbundled system in most scenarios.     

区域性物流园区竞合策略的演化博弈分析

针对我国物流园区发展现状,探讨了区域性物流园区之间的竞合策略。建立了区域性物流园区竞合策略的演化博弈模型,据此分析了物流园区间竞争合作关系演变发展的趋势。研究表明,区域性物流园区之间长期竞争合作演化的结果是完全竞争或完全合作;在一定条件下,物流园区竞合策略选择的动态演化过程收敛于哪一个均衡点受到博弈发生的初始状态的影响,演化的路径和最终状态与转化能力、风险水平以及资源水平密切相关。     

广告盈利模式下网购平台间的竞争对其质量管控力度的影响

当前网购市场中的假冒伪劣现象备受社会关注,作为网购供应链的核心主体,网购平台企业应承担相应质量管控义务。既有文献对平台企业的质量管控进行了有益的探索,文章在此基础之上,探讨广告收入为网购平台主要营收来源时,两个不同规模平台企业间的竞争对其质量管控力度的影响。在双边市场理论框架下,通过构建博弈模型得到如下结果：随着网购平台之间竞争程度的增加,或随着网购平台之间广告宣传替代性的增强,或随着进驻网购平台在线商家数量的增多,每个平台企业均会提高质量管控力度;两个平台企业的质量管控力度随着在线消费者对广告厌恶度的增加均呈倒U型变化趋势。     

Relationships among quasivarieties induced by the min networks on inverse semigroups

Semigroup Forum - A congruence on an inverse semigroup S is determined uniquely by its kernel and trace. Denoting by $$\rho _k$$ and $$\rho _t$$ the least congruence on S having the same kernel and...     

Revenue management for low-cost providers

Low-cost providers have emerged as important players in many service industries, the most predominant being low-cost, or the so-called discount airlines. This paper presents models and results leading toward understanding the revenue management outlook for a discount pricing firm. A framework and model is formulated specifically for the airline industry, but is generalizable to low-cost providers in similar revenue management settings. We formulate an optimal pricing control model for a firm that must underprice to capture a segment of exogenous demand. Two specific model formulations are considered: a continuous deterministic version, and a discrete stochastic version. Structural results are derived for the deterministic case, providing insight into the general form of optimal underpricing policies. The stochastic results support the structural insight from the deterministic solution, and illuminate the effect of randomness on the underpricing policies.     

Subsidy Competition in Networks

This paper investigates a competitive location model on a network with free entry and exit. The given network consists of regions that represent independent jurisdictions. Market entry and exit are sequential. In each stage of the multi-stage game, the regions simultaneously decide what subsidy to offer to a firm should it located within its boundaries. The paper delineates three distinct classes of subsidy policies and examines their effects in a series of computational tests.     

State-dependent routing on symmetric loss networks with trunk reservations. II: Asymptotics,optimal design

We investigate a distributed, state-dependent, dynamic routing strategy for circuit-switched loss networks which we have called Aggregated-Least-Busy-Alternative (ALBA). The networks considered are symmetric and fully connected, the offered calls form Poisson streams and routes have at most two links. In ALBA(K), the states of each link are lumped intoK (K 2) aggregates and the route of each call is determined by local information on the aggregate-states of the links of the alternate routes. The last aggregate is always the set of states reserved for direct traffic and defined by the trunk reservation parameter. The particular case of ALBA in which there is no aggregation is Least-Busy-Alternative (LBA); ALBA(2) represents the other extreme of aggregation. We consider two separate asymptotic scalings based on Fixed Point Models for ALBA(K) which were obtained and investigated in an earlier paper. In the first, it is assumed that the number of network nodes, the offered traffic and trunk group size are all large; their ratios have been chosen to reflect practical interest. The results show that there exists a threshold which delineates fundamentally different behavior: for offered traffic below the threshold, the network loss probability decreases exponentially with increasing network size, while above the threshold the decrease is only polynomial. In the related second asymptotic scaling, the asymptotically optimum trunk reservation parameter is obtained as the solution of a simple equation. Such asymptotically optimal designs are compared to the outputs of exhaustive numerical searches for some realistically sized networks and found to perform very well.Dr. Gibbens' work was done while visiting AT&T Bell Laboratories. His present address: Statistical Laboratory, University of Cambridge, 16 Mill Lane, Cambridge, CB2 1SB, UK.