There is no optimal routing policy for the torus

A routing policy is the method used to select a specific output channel for a message from among a number of acceptable output channels. An optimal routing policy is a policy that maximizes the probability of a message reaching its destination without delays. Optimal routing policies have been proposed for several regular networks, including the mesh and the hypercube. An open problem in interconnection network research has been the identification of an optimal routing policy for the torus. In this paper, we show that there is no optimal routing policy for the torus. Our result is demonstrated by presenting a detailed example in which the best choice of output channel is dependent on the probability of each channel being available. This result settles, in the negative, a conjecture by Wu concerning an optimal routing policy for the torus.     

Optimal dynamic advertising with an adverse exogenous effect on brand goodwill

We propose the model of a firm that advertises a product in a homogeneous market, where a constant exogenous interference is present. Using the framework of Nerlove and Arrow’s advertising model, we assume that the interference acts additively on goodwill production as a negative term. Hence, we allow that the goodwill may become negative and we associate a zero demand with negative goodwill values. We consider a piecewise linear demand function and formulate a nonsmooth optimal-control problem with an infinite horizon. We obtain that an optimal advertising policy exists and takes one of two forms: either a positive and constant advertising effort, or a decreasing effort starting from a positive level and eventually reaching the zero value at a finite exit time. In the former scenario, the demand is always positive and the firm stays in the market in the long run; in the latter, the demand becomes zero in the short run, and afterward, the firm goes out of business. In both cases we have an explicit representation of the optimal control, which is obtained through the study of an auxiliary smooth optimal-control problem. It is interesting that the fundamental choice between staying in the market and going out of business at some time depends both on the interference level and on the initial goodwill level.     

Optimal Channel Choice for Lossy Data Flow Transmission

We consider the optimal control problem for the load of several communication channels defined by independent Markov jump processes. Implicit information on the state of a channel is available in the form of a flow of losses whose intensity is proportional to the controllable load of this channel. The optimized functionals take into account the total throughput of channels and energy costs for data transmission over a fixed interval of time. We obtain optimal filtering equations for joint estimation of channel states. We construct a locally optimal strategy that explicitly depends on the set of state estimates.     

Manufacturer defensive and offensive advertising in competing distribution channels

This paper investigates how two competing manufacturers should invest in defensive and offensive advertising in a two‐segment market and whether they should each adopt a decentralized or an integrated channel if their goal is to maximize total channel profits. We find that manufacturers in decentralized channels can exclusively undertake either of the two types of advertising or combine the two at the equilibrium. In integrated channels, they can either combine the two or exclusively undertake defensive advertising. When multiple equilibria exist, strategies that combine both types of advertising should be preferred to exclusive defensive advertising strategies, which are better than exclusive offensive advertising strategies. Also, total channel profits are higher in decentralized channels than in integrated channels when the brands are moderately or highly substitutable. Conversely, total channel profits of integrated channels are higher than those of decentralized channels in areas where the brands are relatively differentiated and the offensive advertising retaliatory capacity of the rival is stronger. Theoretical and managerial implications of these findings are discussed.     

Co-op advertising and pricing models in manufacturer–retailer supply chains

Cooperative (co-op) advertising plays a significant role in marketing programs in conventional supply chains and makes up the majority of promotional budgets in many product lines for both manufacturers and retailers. Nevertheless, most studies to date on co-op advertising have only assumed that the market demand is only influenced by the advertising level but not in any way by the retail price. That is why our work is concerned with co-op advertising and pricing strategies in distribution channels consisting of a manufacturer and a retailer. Four different models are discussed which are based on three non-cooperative games (i.e., Nash, Stackelberg retailer and Stackelberg manufacturer) and one cooperative game. We identify optimal co-op advertising and pricing strategies for both firms mostly analytically but we have to resort to numerical simulations in one case. Comparisons are then made about various outcomes, especially the profits, for all cases. This leads to consider more specifically the cooperation case in which profits are the highest for both the retailer and the manufacturer, and how they should share the extra joint profit achieved by moving to cooperation. We solve this bargain problem using the Nash bargaining model.     

Online keyword based advertising: Impact of ad impressions on own-channel and cross-channel click-through rates

Keyword-based ads are becoming the dominant form of advertising online as they enable customization and tailoring of messages relevant to potential consumers. Two prominent channels within this sphere are the search channel and the content channel. We empirically examine the interaction between these two channels. Our results indicate significant cannibalization across the two channels as well as significant diminishing returns to impressions within each channel. This suggests that under certain conditions both channels may need to be used to optimize returns to advertising both for advertisers and service providers such as Google. Our game theoretic analysis which builds upon our empirical findings reveals that for intermediate budget values it is optimal to use both channels whereas for very low (very high) budget values it is optimal to use only the content (search) channel. Further as budget increases the advertiser should offer more for ads displayed on the search channel to optimally incentivize the service provider.     

Coordinating the ordering and advertising policies for a single-period commodity in a two-level supply chain

This study deals with the news-vendor problem to the case of a two-level supply chain consisting of one manufacturer and one retailer, and investigates the combined effects of the cooperative advertising mechanism, the return policy and the channel coordination. The manufacturer and the retailer could maintain the potential market size by making some marketing expenditures on some national brand names and invest in local advertising, but with diminishing returns. The decision problem facing the profit-oriented entities in the supply chain is to determine the optimal advertising and inventory policies for maximizing their own profit. Both the non-cooperative policy and the cooperative policy are formulated to offer structural and quantitative insights into the interplay between upstream and downstream entities of the supply chain. In addition, the implications of a profit-sharing mechanism based on achieving a win–win relationship of the channel members was also proposed.     

慢衰落信道环境下中继节点的优化选择方案

在协同通信技术中,中继节点的选择是一个重要的研究方向。在以往的文献中,只考虑了单径信道下的中继节点选择,而在实际情况下,通信信道是多径衰落的。为此,提出了一种多径慢衰落信道环境下的最优中继的选择方案。实验结果显示,利用此方案选出的最优中继节点往往不是传统的只考虑单径情况下所选出的最优中继节点。因此,所提出的方案更符合协同通信中的实际情况,并可在较大程度上提高系统的性能。     

Optimal transmission schemes for parallel and fading Gaussian broadcast channels with an energy harvesting rechargeable transmitter

We consider an energy harvesting transmitter sending messages to two users over parallel and fading Gaussian broadcast channels. Energy required for communication arrives (is harvested) at the transmitter and a finite-capacity battery stores it before being consumed for transmission. Under off-line knowledge of energy arrival and channel fading variations, we obtain the trade-off between the performances of the users by characterizing the maximum departure region in a given interval. We first analyze the transmission with an energy harvesting transmitter over parallel broadcast channels. We show that the optimal total transmit power policy that achieves the boundary of the maximum departure region is the same as the optimal policy for the non-fading broadcast channel, which does not depend on the priorities of the users, and therefore is the same as the optimal policy for the non-fading scalar single-user channel. The optimal total transmit power can be found by a directional water-filling algorithm. The optimal splitting of the power among the parallel channels is performed in each epoch separately. Next, we consider fading broadcast channels and obtain the transmission policies that achieve the boundary of the maximum departure region. The optimal total transmit power allocation policy is found using a specific directional water-filling algorithm for fading broadcast channels. The optimal power allocation depends on the priorities of the users unlike in the case of parallel broadcast channels. Finally, we provide numerical illustrations of the optimal policies and maximum departure regions for both parallel and fading broadcast channels.     

Optimal channel switching in multiuser systems under average capacity constraints

In this paper, the optimal channel switching problem is studied for average capacity maximization in the presence of multiple receivers in the communication system. First, the optimal channel switching problem is proposed for average capacity maximization of the communication between the transmitter and the secondary receiver while fulfilling the minimum average capacity requirement of the primary receiver and considering the average and peak power constraints. Then, an alternative equivalent optimization problem is provided and it is shown that the solution of this optimization problem satisfies the constraints with equality. Based on the alternative optimization problem, it is obtained that the optimal channel switching strategy employs at most three communication links in the presence of multiple available channels in the system. In addition, the optimal strategies are specified in terms of the number of channels employed by the transmitter to communicate with the primary and secondary receivers. Finally, numerical examples are provided in order to verify the theoretical investigations.     

Composite synchronization in parallel discrete-event simulation

This paper considers a technique for composing global (barrier-style) and local (channel scanning) synchronization protocols within a single parallel discrete-event simulation. Composition is attractive because it allows one to tailor the synchronization mechanism to the model being simulated. We first motivate the problem by showing the large performance gap that can be introduced by a mismatch of model and synchronization method. Our solution calls for each channel between submodels to be classified as synchronous or asynchronous. We mathematically formulate the problem of optimally classifying channels and show that, in principle, the optimal classification can be obtained in time proportional to max{C×log C, V×N}, where C is the number of channels, V the number of unique minimal delays on those channels, and N is the number of submodels. We then demonstrate an implementation which finds an optimal solution at runtime and consider its performance on network topologies, including one of the global Internet at the autonomous system level. We find that the automated method effectively determines channel assignments that maximize performance     

Organizational strategy development in distribution channel management using fuzzy AHP and hierarchical fuzzy TOPSIS

Distribution channel management not only consists of choosing distribution channels. In fact, probably the most difficult phase of the distribution management starts after this choice. Determining an appropriate organization strategy for distribution channel management is like a problem of concern to marketing practitioners and academics as well in this phase. In this study, the organization strategy of distribution channel management is developed using fuzzy analytic hierarchy process (FAHP) and hierarchical fuzzy TOPSIS (HFTOPSIS) for an edible-vegetable oils manufacturer firm operating in Turkey. The company distributes its products all over the country. Due to the complex structure of the distribution network, the company wants to decide the organization strategy to manage the distribution channels. In this paper, the methods of FAHP and HFTOPSIS for evaluating and selecting among the five organization strategy models for distribution channel management of vegetable oil manufacturer have been presented. The proposed models include determinants of distribution channel management for edible-vegetable oil industry; (i) customer profile, (ii) distributor reliability, (iii) the position of competitors in market, and (iv) managerial and financial perspective. Using FAHP and HFTOPSIS, hybrid based strategy (KBS), which has the greatest desirability index value after the evaluation among the five alternatives is found as the best choice. Thus, the case of the vegetable oil manufacturer company provides the researchers and practitioners to understand in a better way the importance of developing organization strategy in channel management from a practical point of view.     

Maximization of average number of correctly received symbols over multiple channels in the presence of idle periods

In this study, optimal channel switching (time sharing) strategies are investigated under average power and cost constraints for maximizing the average number of correctly received symbols between a transmitter and a receiver that are connected via multiple flat-fading channels with additive Gaussian noise. The optimal strategy is shown to correspond to channel switching either among at most three different channels with full channel utilization (i.e., no idle periods), or between at most two different channels with partial channel utilization. Also, it is stated that the optimal solution must operate at the maximum average power and the maximum average cost, which facilitates low-complexity approaches for obtaining the optimal strategy. For two-channel strategies, an upper bound is derived, in terms of the parameters of the employed channels, on the ratio between the optimal power levels. In addition, theoretical results are derived for characterizing the optimal solution for channel switching between two channels, and for comparing performance of single channel strategies. Sufficient conditions that depend solely on the systems parameters are obtained for specifying when partial channel utilization cannot be optimal. Furthermore, the proposed optimal channel switching problem is investigated for logarithmic cost functions, and various theoretical results are obtained related to the optimal strategy. Numerical examples are presented to illustrate the validity of the theoretical results.     

Profit maximization through advertising: A nonzero sum differential game approach

This paper deals with the problem of the competition between two firms who sell substitutable products. Each firm wants to maximize its own profits. A firm's share of the market is influenced by its advertising and the advertising of its competitor. The problem is modeled as a nonzero sum differential game. Various solution concepts are applied and the corresponding "optimal" advertising rates obtained.     

需求信息不对称下的双渠道供应链合作广告投资决策分析

研究制造商主导的Stackelberg 博弈下双渠道供应链的合作广告策略, 分析信息不对称及双渠道对供应链合作广告投资决策的影响. 研究表明, 零售商在具有需求信息优势时会谎报需求信息, 并且在一定条件下其谎报决策会降低制造商的利润, 但能提高供应链的利润, 这种情况下制造商无法通过激励合同促使零售商共享信息. 另外, 在最优合作广告策略下, 当直销渠道与分销渠道所占市场份额的分配比例小于一定值时, 制造商采取双渠道会使供应链参与者均受益.

     

Optimal asynchronous agreement and leader election algorithm for complete networks with Byzantine faulty links

Summary.  We consider agreement and leader election on asynchronous complete networks when the processors are reliable, but some of the channels are subject to failure. Fischer, Lynch, and Paterson have already shown that no deterministic algorithm can solve the agreement problem on asynchronous networks if any processor fails during the execution of the algorithm. Therefore, we consider only channel failures. The type of channel failure we consider in this paper is Byzantine failure, that is, channels fail by altering messages, sending false information, forging messages, losing messages at will, and so on. There are no restrictions on the behavior of a faulty channel. Therefore, a faulty channel may act as an adversary who forges messages on purpose to prevent the successful completion of the algorithm. Because we assume an asynchronous network, the channel delays are arbitrary. Thus, the faulty channels may not be detectable unless, for example, the faulty channels cause garbage to be sent. We present the first known agreement and leader election algorithm for asynchronous complete networks in which the processors are reliable but some channels may be Byzantine faulty. The algorithm can tolerate up to [n−22] faulty channels, where n is the number of processors in the network. We show that the bound on the number of faulty channels is optimal. When the processors terminate their corresponding algorithms, all the processors in the network will have the same correct vector, where the vector contains the private values of all the processors. Received: May 1994/Accepted: July 1995     

Pricing display ads and contextual ads: Competition,acquisition, and investment

Most websites are simultaneously supported by display advertising and contextual advertising. In this paper, we develop an economic model to examine the profitability of these two ad types in both a monopolistic market and duopolistic market, identifying the influence of impression benefit and click benefit. We find that in the duopolistic market a rival channel’s professional ability to enhance a visitor’s impression is beneficial to the channel offering contextual advertising. We also find that the strength of a search engine is limited in the duopolistic market; therefore, acquisition becomes a prime strategy to reveal the value of contextual advertising.     

On spectrum sharing games

Efficient spectrum-sharing mechanisms are crucial to alleviate the bandwidth limitation in wireless networks. In this paper, we consider the following question: can free spectrum be shared efficiently? We study this problem in the context of 802.11 or WiFi networks. Each access point (AP) in a WiFi network must be assigned a channel for it to service users. There are only finitely many possible channels that can be assigned. Moreover, neighboring access points must use different channels so as to avoid interference. Currently these channels are assigned by administrators who carefully consider channel conflicts and network loads. Channel conflicts among APs operated by different entities are currently resolved in an ad hoc manner (i.e., not in a coordinated way) or not resolved at all. We view the channel assignment problem as a game, where the players are the service providers and APs are acquired sequentially. We consider the price of anarchy of this game, which is the ratio between the total coverage of the APs in the worst Nash equilibrium of the game and what the total coverage of the APs would be if the channel assignment were done optimally by a central authority. We provide bounds on the price of anarchy depending on assumptions on the underlying network and the type of bargaining allowed between service providers. The key tool in the analysis is the identification of the Nash equilibria with the solutions to a maximal coloring problem in an appropriate graph. We relate the price of anarchy of these games to the approximation factor of local optimization algorithms for the maximum k-colorable subgraph problem. We also study the speed of convergence in these games.     

Fault tolerant computing and reliable communication: A unified approach

We define and study varying-structure linear systems (VLS) over finite Abelian groups. All the VLS computational procedures are very fast with upper bounds on the number of computer operations similar to that of fast Fourier transform algorithms over groups. Specially designed VLS process n-vectors in linear (in n) number of computer operations. These systems are used in problems related to information channels (optimal estimation of noise-corrupted signals) and computation channels (error detection). We consider problems of optimal synthesis procedures of such systems relative to two easily computed criteria. The best approximation problem of classical systems by VLS also is studied. It is shown that the VLS constitute a class of suboptimal systems from which approximations can be found to a given information and/or computation channel. The approach chosen for these two channel types is unified. Information channel problems are usually solved in Euclidean type norms, whereas computation channel problems are dealt with via the generalized Hamming distance.     

Structural Properties of Optimal Transmission Policies Over a Randomly Varying Channel

We consider the problem of transmitting packets over a randomly varying point to point channel with the objective of minimizing the expected power consumption subject to a constraint on the average packet delay. By casting it as a constrained Markov decision process in discrete time with time-averaged costs, we prove structural results about the dependence of the optimal policy on buffer occupancy, number of packet arrivals in the previous slot and the channel fading state for both i.i.d. and Markov arrivals and channel fading. The techniques we use to establish such results: convexity, stochastic dominance, decreasing-differences, are among the standard ones for the purpose. Our main contribution, however, is the passage to the average cost case, a notoriously difficult problem for which rather limited results are available. The novel proof techniques used here are likely to have utility in other stochastic control problems well beyond their immediate application considered here.