Stochastic analysis of a single server retrial queue with general retrial times

Retrial queueing systems are widely used in teletraffic theory and computer and communication networks. Although there has been a rapid growth in the literature on retrial queueing systems, the research on retrial queues with nonexponential retrial times is very limited. This paper is concerned with the analytical treatment of an M/G/1 retrial queue with general retrial times. Our queueing model is different from most single server retrial queueing models in several respectives. First, customers who find the server busy are queued in the orbit in accordance with an FCFS (first‐come‐first‐served) discipline and only the customer at the head of the queue is allowed for access to the server. Besides, a retrial time begins (if applicable) only when the server completes a service rather upon a service attempt failure. We carry out an extensive analysis of the queue, including a necessary and sufficient condition for the system to be stable, the steady state distribution of the server state and the orbit length, the waiting time distribution, the busy period, and other related quantities. Finally, we study the joint distribution of the server state and the orbit length in non‐stationary regime. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 561–581, 1999     

An economic selective assembly procedure for two mating components with equal variance

An economic procedure of selective assembly is proposed when a product is composed of two mating components. The major quality characteristic of the product is the clearance between the two components. The components are divided into several classes prior to assembly. The component characteristics are assumed to be independently and normally distributed with equal variance. The procedure is designed so that the proportions of both components in their corresponding classes are the same. A cost model is developed based on a quadratic loss function and methods of obtaining the optimal class limits as well as the optimal number of classes are provided. Formulas for obtaining the proportion of rejection and the unavailability of mating components are also provided. The proposed model is compared with the equal width and the equal area partitioning methods using a numerical example. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 809–821, 1999     

Inventory policies for a make‐to‐order system with a perishable component and fixed ordering cost

We consider a make‐to‐order production system where two major components, one nonperishable (referred to as part 1) and one perishable (part 2), are needed to fulfill a customer order. In each period, replenishment decisions for both parts need to be made jointly before demand is realized and a fixed ordering cost is incurred for the nonperishable part. We show that a simple (s_n,S,S) policy is optimal. Under this policy, S along with the number of backorders at the beginning of a period if any and the availability of the nonperishable part (part 1) determines the optimal order quantity of the perishable part (part 2), while (s_n,S) guide when and how much of part 1 to order at each state. Numerical study demonstrates that the benefits of using the joint replenishment policy can be substantial, especially when the unit costs are high and/or the profit margin is low. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

Economic and environmental impacts of vertical and horizontal competition and integration

We explore the economic and environmental impacts of market structures (competition or integration at vertical and horizontal levels). We consider a bilateral duopoly consisting of two manufacturers and two retailers in which each manufacturer offers a wholesale price contract to the respective retailer. The manufacturers decide on wholesale prices and abatement efforts concerning pollution emissions related to manufacturing processes, whereas the retailers compete in quantities in the consumer market. To understand the comprehensive effects of market structures on economic competitiveness and environmental sustainability, we examine a measure of eco‐friendly social welfare, which is the ratio of social welfare and environmental pollution. Interestingly, we find that the market structures that have been believed to be more efficient are less efficient from a broader perspective: (1) double marginalization can generate higher eco‐friendly social welfare, and (2) horizontal competition between firms can result in lower eco‐friendly social welfare. Although vertical integration and horizontal competition yield greater social welfare by facilitating more production activities, these market structures often fail to induce sufficient abatement efforts to balance the polluting effect of the large volume, resulting in more significant environmental degradation. We also show that, despite the pollution‐curbing effect, higher emission penalties can result in less eco‐friendly social welfare. They can even curtail the abatement efforts of firms under particular circumstances. When products become more substitutable, the eco‐friendly social welfare can decrease depending upon the market structure.     

Planning gamma accelerated degradation tests with two accelerating variables

Gamma accelerated degradation tests (ADT) are widely used to assess timely lifetime information of highly reliable products with degradation paths that follow a gamma process. In the existing literature, there is interest in addressing the problem of deciding how to conduct an efficient, ADT that includes determinations of higher stress‐testing levels and their corresponding sample‐size allocations. The existing results mainly focused on the case of a single accelerating variable. However, this may not be practical when the quality characteristics of the product have slow degradation rates. To overcome this difficulty, we propose an analytical approach to address this decision‐making problem using the case of two accelerating variables. Specifically, based on the criterion of minimizing the asymptotic variance of the estimated q quantile of lifetime distribution of the product, we analytically show that the optimal stress levels and sample‐size allocations can be simultaneously obtained via a general equivalence theorem. In addition, we use a practical example to illustrate the proposed procedure.     

Maintaining systems with heterogeneous spare parts

We consider the problem of optimally maintaining a stochastically degrading, single‐unit system using heterogeneous spares of varying quality. The system's failures are unannounced; therefore, it is inspected periodically to determine its status (functioning or failed). The system continues in operation until it is either preventively or correctively maintained. The available maintenance options include perfect repair, which restores the system to an as‐good‐as‐new condition, and replacement with a randomly selected unit from the supply of heterogeneous spares. The objective is to minimize the total expected discounted maintenance costs over an infinite time horizon. We formulate the problem using a mixed observability Markov decision process (MOMDP) model in which the system's age is observable but its quality must be inferred. We show, under suitable conditions, the monotonicity of the optimal value function in the belief about the system quality and establish conditions under which finite preventive maintenance thresholds exist. A detailed computational study reveals that the optimal policy encourages exploration when the system's quality is uncertain; the policy is more exploitive when the quality is highly certain. The study also demonstrates that substantial cost savings are achieved by utilizing our MOMDP‐based method as compared to more naïve methods of accounting for heterogeneous spares.     

Some order relations in closed networks of queues with multiserver stations

Consider a closed network of queues of the “product-form” type, where each station has s servers (s ≥ 1 is identical for all stations). We show that the throughput function of the network is Schur concave with respect to the loading of the stations and arrangement increasing with respect to the assignment of server groups. Consequently, different loading/assignment policies can be compared under majorization/arrangement orderings and their relative merits decided according to the yields of throughput. The results can be used to support planning decisions in computer and production systems which are modeled as closed networks of queues.     

Why provoke? the Sino-US competition in East Asia and North Korea’s strategic choice

This article seeks to make sense of North Korean provocations in light of the Sino-US strategic competition in post-Cold War East Asia, where such variables as China’s rise, US’s pivot to Asia, and growing Sino-ROK economic ties are driving the strategic choices of major states in the region. The article examines the main motivations behind Pyongyang’s provocations since the end of the Cold War, discusses their implications for the Sino-US strategic competition in East Asia, and offers predictions about the future of North Korean provocations. The central thesis of the article is that Pyongyang has exploited the Sino-US strategic competition in East Asia for its regime survival. By raising North Korea’s strategic value to China, the intensifying Sino-US competition allows Pyongyang to continue provocations, regardless of Beijing’s explicit opposition.     

On efficiency of multistage channel with bargaining over wholesale prices

This article considers a multistage channel with deterministic price‐sensitive demand. Two systems for pricing decisions, that is, the bargaining system and the leader‐follower system, are compared. We characterize the necessary and sufficient conditions on the power structure, under which the solution of the bargaining system Pareto dominates that of the leader‐follower system. Also, under such conditions, we give a tight upper bound of channel efficiency of the bargaining system, which converges to 100% channel efficiency as the number of stages increases to infinity. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 449–459, 2016     

Minimal LST representations of MAP(n)s: Moment fittings and queueing approximations

A Markovian arrival process of order n, MAP(n), is typically described by two n × n transition rate matrices in terms of rate parameters. While it is straightforward and intuitive, the Markovian representation is redundant since the minimal number of parameters is n² for non‐redundant MAP(n). It is well known that the redundancy complicates exact moment fittings. In this article, we present a minimal and unique Laplace‐Stieltjes transform (LST) representations for MAP(n)s. Even though the LST coefficients vector itself is not a minimal representation, we show that the joint LST of stationary intervals can be represented with the minimum number of parameters. We also propose another minimal representation for MAP(3)s based on coefficients of the characteristic polynomial equations of the two transition rate matrices. An exact moment fitting procedure is presented for MAP(3)s based on two proposed minimal representations. We also discuss how MAP(3)/G/1 departure process can be approximated as a MAP(3). A simple tandem queueing network example is presented to show that the MAP(3) performs better than the MAP(2) in queueing approximations especially under moderate traffic intensities. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 549–561, 2016