Allocation of buffer capacities in queueing networks with arbitrary topologies

Two algorithms are developed to allocateM buffers toN service stations connected arbitrarily in a feed-forward manner. All service times and the interarrival times are assumed to be exponentially distributed. Both methodologies are easy-to-use tools to explore alternative buffer storage configurations and parameter settings during the initial design stages of production systems, communications networks, and flexible manufacturing systems.This research was done while the author was on a sabbatical leave of absence at North Carolina State University, Raleigh, North Carolina.     

Waiting times in queueing networks with a single shared server

We study a queueing network with a single shared server that serves the queues in a cyclic order. External customers arrive at the queues according to independent Poisson processes. After completing service, a customer either leaves the system or is routed to another queue. This model is very generic and finds many applications in computer systems, communication networks, manufacturing systems, and robotics. Special cases of the introduced network include well-known polling models, tandem queues, systems with a waiting room, multi-stage models with parallel queues, and many others. A complicating factor of this model is that the internally rerouted customers do not arrive at the various queues according to a Poisson process, causing standard techniques to find waiting-time distributions to fail. In this paper, we develop a new method to obtain exact expressions for the Laplace–Stieltjes transforms of the steady-state waiting-time distributions. This method can be applied to a wide variety of models which lacked an analysis of the waiting-time distribution until now.     

Profit maximization in flexible serial queueing networks

We analyze the tradeoff between efficiency and service quality in tandem systems with flexible servers and finite buffers. We reward efficiency by assuming that a revenue is earned each time a job is completed, and penalize poor service quality by incorporating positive holding costs. We study the dynamic assignment of servers to tasks with the objective of maximizing the long-run average profit. For systems of arbitrary size, structured service rates, and linear or nonlinear holding costs, we determine the server assignment policy that maximizes the profit. For systems with two stations, two servers with arbitrary service rates, and linear holding costs, we show that the optimal server assignment policy is of threshold type and determine the value of this threshold as a function of the revenue and holding cost. The threshold can be interpreted as the best possible buffer size, and hence our results prove the equivalence of addressing service quality via a holding cost and via limiting the buffer size. Furthermore, we identify the optimal buffer size when each buffer space comes at a cost. We provide numerical results that suggest that the optimal policy also has a threshold structure for nonlinear holding costs. Finally, for larger systems with arbitrary service rates, we propose effective server assignment heuristics.     

Integer programming models for maximizing parallel transmissions in wireless networks

In radio communications, a set of links that can transmit in parallel with a tolerable interference is called a compatible set. Finding a compatible set with maximum weighted revenue of the parallel transmissions is an important subproblem in wireless network management. For the subproblem, there are two basic approaches to express the signal to interference plus noise ratio (SINR) within integer programming, differing in the number of variables and the quality of the upper bound given by linear relaxations. To our knowledge, there is no systematic study comparing the effectiveness of the two approaches. The contribution of the paper is two-fold. Firstly, we present such a comparison, and, secondly, we introduce matching inequalities improving the upper bounds as compared to the two basic approaches. The matching inequalities are generated within a branch-and-cut algorithm using a minimum odd-cut procedure based on the Gomory-Hu algorithm. The paper presents results of extensive numerical studies illustrating our statements and findings.     

Measuring and rewarding flexibility in collaborative distribution,including two-partner coalitions

Horizontal collaboration among shippers is gaining traction as a way to increase logistic efficiency. The total distribution cost of a logistic coalition is generally between 9% and 30% lower than the sum of costs of each partner distributing separately. However, the coalition gain is highly dependent on the flexibility that each partner allows in its delivery terms. Flexible delivery dates, flexible order sizes, order splitting rules, etc., allow the coalition to exploit more opportunities for optimization and create better and cheaper distribution plans.     

An arc-exchange decomposition method for multistage dynamic networks with random arc capacities

Multistage dynamic networks with random arc capacities (MDNRAC) have been successfully used for modeling various resource allocation problems in the transportation area. However, solving these problems is generally computationally intensive, and there is still a need to develop more efficient solution approaches. In this paper, we propose a new heuristic approach that solves the MDNRAC problem by decomposing the network at each stage into a series of subproblems with tree structures. Each subproblem can be solved efficiently. The main advantage is that this approach provides an efficient computational device to handle the large-scale problem instances with fairly good solution quality. We show that the objective value obtained from this decomposition approach is an upper bound for that of the MDNRAC problem. Numerical results demonstrate that our proposed approach works very well.     

Deadlock properties of queueing networks with finite capacities and multiple routing chains

Blocking in queueing network models with finite capacities can lead to deadlock situations. In this paper, deadlock properties are investigated in queueing networks with multiple routing chains. The necessary and sufficient conditions for deadlockfree queueing networks with blocking are provided. An optimization algorithm is presented for finding deadlock-free capacity assignments with the least total capacity. The optimization algorithm maps the queueing network into a directed graph and obtains the deadlock freedom conditions from a specified subset of cycles in the directed graph. In certain network topologies, the number of deadlock freedom conditions can be large, thus, making any optimization computationally expensive. For a special class of topologies, so-calledtandem networks, it is shown that a minimal capacity assignment can be directly obtained without running an optimization algorithm. Here, the solution to the minimal capacity assignment takes advantage of the regular topology of tandem networks.This work was supported by the National Science Foundation under Grant No. CCR-90-11981.     

Bargaining sets with small coalitions

We study two alternative definitions of the bargaining set in large (atomless) economies; the local bargaining by MasColell (1989) and the global bargaining set by Vind (1992). We alter these definitions to limit the size of the permitted size of the involved coalitions. It turns out that the local bargaining set becomes very large, whereas the global bargaining set is unaltered.     

Self-enforcing coalitions with power accumulation

Agents endowed with power compete for a divisible resource by forming coalitions with other agents. The coalition with the greatest power wins the resource and divides it among its members. The agents’ power increases according to their share of the resource.We study two models of coalition formation where winning agents accumulate power and losing agents may participate in further coalition formation processes. An axiomatic approach is provided by focusing on variations of two main axioms: self-enforcement, which requires that no further deviation happens after a coalition has formed, and rationality, which requires that agents pick the coalition that gives them their highest payoff. For these alternative models, we determine the existence of stable coalitions that are self-enforcing and rational for two traditional sharing rules. The models presented in this paper illustrate how power accumulation, the sharing rule, and whether losing agents participate in future coalition formation processes, shape the way coalitions will be stable throughout time.     

The fuzzy core in games with fuzzy coalitions

In this paper, the fuzzy core of games with fuzzy coalition is proposed, which can be regarded as the generalization of crisp core. The fuzzy core is based on the assumption that the total worth of a fuzzy coalition will be allocated to the players whose participation rate is larger than zero. The nonempty condition of the fuzzy core is given based on the fuzzy convexity. Three kinds of special fuzzy cores in games with fuzzy coalition are studied, and the explicit fuzzy core represented by the crisp core is also given. Because the fuzzy Shapley value had been proposed as a kind of solution for the fuzzy games, the relationship between fuzzy core and the fuzzy Shapley function is also shown. Surprisingly, the relationship between fuzzy core and the fuzzy Shapley value does coincide, as in the classical case.     

有限制结盟的NTU对策解

对有限制结盟的NTU对策提出一种分配形式,即RC解,研究了这个解与对应的TU对策的有限制结盟边际贡献值之间的关系,同时给出RC解的刻划公理.     

Sustainable coalitions in the commons

It is well known that the lack of cooperation among agents harvesting a renewable resource is critical for its sustainable management. The present paper gives insights into the complex balance between coalition structures, resource states or dynamics and the agent heterogeneity necessary to avoid bio-economic collapses. A model bringing together coalition games and a viability approach is proposed to focus on the compatibility between bio-economic constraints and exploited common stock dynamics. The extent to which cooperation promotes sustainability is examined. Our results suggest that the stability of the grand coalition occurs for large enough stocks. By contrast, for lower levels of resources, the most efficient user plays the role of veto player.     

Optimizing two-level reverse distribution networks with hybrid memetic algorithms

In a Two-Level Reverse Distribution Network, products are returned from customers to manufacturers through collection and refurbishing sites. The costs of the reverse chain often overtake the costs of the forward chain by many times. With some known algorithms for the problem as reference, we propose a hybrid memetic algorithm that uses linear programming and a heuristic for defining routes. Moreover, we describe heuristics for deciding locations, algorithms to define routes for the products, and problem-specific genetic operators. Memetic algorithms have returned the best results for all instances.     

模糊联盟合作对策的平均树解

给出图对策中平均树解的拓展形式, 证明其是满足分支有效性和分支公平性的唯一解. 针对具有模糊联盟的图对策, 提出了一种模糊分配, 即模糊平均树解. 当模糊联盟图对策为完全图对策时, 模糊平均树解等于模糊Shapley值. 最后, 讨论了模糊平均树解与模糊联盟核心之间的关系, 并进行了实例论证.     

A shapley value for games with restricted coalitions

A restriction is a monotonic projection assigning to each coalition of a finite player setN a subcoalition. On the class of transferable utility games with player setN, a Shapley value is associated with each restriction by replacing, in the familiar probabilistic formula, each coalition by the subcoalition assigned to it. Alternatively, such a Shapley value can be characterized by restricted dividends. This method generalizes several other approaches known in literature. The main result is an axiomatic characterization with the property that the restriction is determined endogenously by the axioms.     

Preferred coalitions in cooperative differential games

There are many interesting situations which can be described by anN-person general-sum differential game. Such games are characterized by the fact that the strategy of each player depends upon reasonable assumptions about the strategies of the remaining players; and, thus, these games cannot be considered asN uncoupled optimal control problems. In such cases, we say that the game is not strictly competitive, but involves a mutual interest which makes it possible for all of the players to reduce their costs by cooperating with one another, provided the resulting agreement can be enforced. When cooperation is allowed and there are more than two players, there is always the question of whether all possible subcoalitions will be formed with equal ease. This work considers the situation in which a particular subcoalition is preferred. A theory of general-sum games with preferred coalitions is presented, together with constructive examples of alternative approaches which are unsatisfactory.     

Estimating completion-time distribution in stochastic activity networks

This paper deals with simulation-based estimation of the probability distribution for completion time in stochastic activity networks. These distribution functions may be valuable in many applications. A simulation method, using importance-sampling techniques, is presented for estimation of the probability distribution function. Separating the state space into two sets, one which must be sampled and another which need not be, is suggested. The sampling plan of the simulation can then be decided after the probabilities of the two sets are adjusted. A formula for the adjustment of the probabilities is presented. It is demonstrated that the estimator is unbiased and the upper bound of variance minimized. Adaptive sampling, utilizing the importance sampling techniques, is discussed to solve problems where there is no information or more than one way to separate the state space. Examples are used to illustrate the sampling plan.