This paper considers the problem of determining the optimal ordering quantity for a perishable product to be sold over a finite sales horizon with a dynamic pricing policy. To date, most models developed to study a dynamic pricing policy for perishable products assume that the salvage value is nonnegative. In this model we allow the salvage value to be either a nonnegative or negative value. We derive the conditions under which the optimal ordering quantity takes either a zero value or finite value greater than zero. Moreover, we demonstrate the existence of a shortest sales horizon under a condition for which ordering of the product is profitable if the seller's planned sales horizon is longer than the shortest sales horizon.

View full abstract

This paper considers the characteristics of block-level success and loss runs for streaming services over wired-wireless networks in which forward error correction (FEC) is employed for packet-loss resilience. We develop a single-server queueing model where the packet-transmission process over a wireless link is modeled by a Markovian service process (MSP) with two states "Good" and "Bad". The queueing system has two input processes: a general renewal input process and a Poisson one. The former represents a streaming-packet flow, while the latter is for background traffic multiplexed at the queue. We investigate the dynamics of the system state during the interval from the arrival epoch of the first packet of the block to that of the last one, deriving the block-loss (resp. block-success) run distribution, i.e., the probability distribution of the number of consecutive block loss (resp. success). The analytical model is validated by trace-driven simulation experiments. Numerical examples show that when the traffic intensity is high, the moments of block-level loss and success runs are significantly affected by the volume of background traffic and the FEC redundancy, rather than the system capacity.

View full abstract

In a decision-making process, one finds that there are alternatives which can be categorized into several groups, based on his or her perspectives, and/or on expected outcome, such as whether his or her choice brings about gains or losses, or that such a choice is right or wrong. Besides, there are many cases with a dilemma where it is hard to select the best choice through transitive relations. This paper presents a new method to dissolve this dilemma by using ANP (Analytic Network Process) with a newly defined criteria matrix. The case of the super-matrix of ANP is examined in an alternative matrix with a dilemma. The paper shows mathematically that the eigenvector of the super-matrix serves as a solution to this simple dilemma, describes the proposed method, and attempts to apply this method to other dilemmas. The proposed method is limited to up to three alternatives.

View full abstract

We consider a stationary multi-class FIFO M/G/1 queue with exponential working vacations, where a server works at two different processing rates. There are K classes of customers, and the arrival rates and the distributions of the amount of service requirements of arriving customers depend on both their customer classes and the server state. When the system becomes empty, the server takes a working vacation, during which customers are served at processing rate γ (γ > 0). If the system is empty at the end of the working vacation, the server takes another working vacation. On the other hand, if a customer is being served at the end of the working vacation, the server switches its processing rate to one and continues to serve customers in a preemptive-resume manner, until the system becomes empty. For this queue, we derive various quantities of interest, including the Laplace-Stieltjes transforms of the actual waiting time and sojourn time distributions, and the joint transform of the numbers of customers and the amounts of unfinished work in respective classes. As by-products, we also obtain various results of a stationary multi-class FIFO M/G/1 queue with Poisson disasters.

View full abstract

In this paper, we propose three O(n_0S(m,n)) algorithms for finding the shortest paths from a vertex in a conservative network with edges of negative length, where S(m,n) is the complexity of Dijkstra's method for a digraph with m edges and n vertices, and n_0 is the number of vertices incident to negative edges. Our study is motivated by S. Fujishige's method, which has a running time that is similar to that of our proposed method. He dealt with the problem of, when the given length function is decreased, updating the shortest paths from all the vertices in a vertex set to all of the given vertices, which is a problem slightly different from ours. His contribution was to solve the problem by applying a simple Dijkstra's method with less initial data than those of a previously proposed algorithm by S. Goto and A. Sangiovanni-Vincentelli. Fujishige introduced the subproblem of computing the shortest paths from a vertex v, subject to the constraint that negative edges are only contained in edges incident to v, and pointed out that the problem can be solved by consecutive applications of Dijkstra's method to a series of such subproblems, given the length of the shortest path between each pair of vertices as prior information. Our approaches are more general purpose than Fujishige's. In fact, ours are not limited to only updating the shortest paths, but also require no such prior information. Each of our algorithms also makes use of the concept of reduced length functions that he employed. We further show that when our algorithms incorporate an additional routine, they only apply Dijkstra's method at most n_0/2 times for a specific class of instances whose subgraphs induced by negative edges are undirected forests.

View full abstract