We show that several truncation properties of queueing systems are consequences of a simple property of censored stochastic processes. We first consider a discrete-time stochastic process and show that its censored process has a truncated stationary distribution. When the stochastic process has continuous time, we present a similar result under the additional condition that the process is locally balanced. We apply these results to single-server batch arrival batch service queues with finite buffers and queueing networks with finite buffers and batch movements, and extend the well-known results on truncation properties of the MX/G/1/k queues and queueing networks with jump-over blocking.

We consider a K-node queueing system sharing a setup server. Each node has a node server, a finite buffer, and a service position. Each job in the buffer at a node requires a setup by the setup server to receive service from the node server at the service position. The arrival process of jobs at each node is Poisson, the distribution of node service times at each node is general, and the setup times have a common exponential distribution. The setup server behaves like M setup servers (i.e., the server can simultaneously process up to M jobs). We consider two setup mechanisms by the setup server. One is that for a setup of job at each node, both the waiting position (occupied by the job) and service position are used. The other is that only the service position is used for a setup. The model operating under the former or latter is referred to as Model I or II, respectively. For each node in Model I or II, we construct a corresponding setup server queue (CSQ). We show that the stationary distribution of Model I or II is given by a product form of the stationary distributions of CSQs.

The linear k-within-(r, s)-out-of-(m, n):F lattice system consists of mn components arranged in m rows and n columns and fails whenever there is at least one rectangle of dimension r × s which contains k or more failed components. We propose recursive formulas for the calculation of the linear k-within-(r, s)-out-of-(m, n):F lattice system. The computing complexity of the system reliability using the recursive formulas is O((n − s)ms+1 + m2s) for r = m and O((r + 1)rs(m−r+1)[(n − s)m + 2r(s−1)ms]) for r < m.

In this paper, we introduce and analyze simple, new inspection policies for maintaining deteriorating equipment with non-self-announcing failures. These policies utilize information from the inspection/repair history as well as the system lifetime distribution to schedule future inspections. Numerical results indicate that the policies can significantly outperform standard (periodic) maintenance strategies by providing higher availability for a given inspection rate.

In this paper, we study the dependence properties of spacings. It is proved that if X1,..., Xn are exchangeable random variables which are TP2 in pairs and their joint density is log-convex in each argument, then the spacings are MTP2 dependent. Next, we consider the case of independent but nonhomogeneous exponential random variables. It is shown that in this case, in general, the spacings are not MTP2 dependent. However, in the case of a single outlier when all except one parameters are equal, the spacings are shown to be MTP2 dependent and, hence, they are associated. A consequence of this result is that in this case, the variances of the order statistics are increasing. It is also proved that in the case of the multiple-outliers model, all consecutive pairs of spacings are TP2 dependent.

Some class properties of the used better (worse) than aged [UBA (UWA)] and the used better (worse) than aged in expectation [UBAE (UWAE)] classes of lifetime distributions are considered. Relationships with the decreasing (increasing) mean residual lifetime [DMRL (IMRL)] class and the decreasing (increasing) variance residual lifetime [DVRL (IVRL)] class are established. Discrete UBA and UWA distributions are introduced and studied. Characterizations of UBA and UWA distributions are derived by using discrete aging properties of mixed Poisson distributions. Applications of these results to queueing theory and ruin are then considered. In particular, preservation of UBA (UWA) and UBAE (UWAE) under a transform of life distributions is given.

In a renewal process, the interarrival times are independent and identically distributed, and in a renewal reward process, the pairs of reward and interarrival time are i.i.d. Many useful results hold for these processes. This paper relaxes the assumption of identical distributions while keeping the assumption of independence. This paper explores the properties of the mean average number of occurrence of events and the mean average reward on any finite time interval. The paper also discusses the limiting properties of these two quantities and extends many results from the renewal process and renewal reward process to the more general counting process and reward sequence.

Motivated by many applications in production planning, system reliability, queueing networks, and wireless communication, this work is devoted to singularly perturbed Markov chains with finite states. Focusing on nonstationary processes with the inclusion of transient states, asymptotic error bounds of a sequence of suitably scaled occupation measures are derived. The main tools used include martingales and differential equations. The results are useful for analyzing structural properties of the underlying Markov chains and for designing nearly optimal and hierarchical controls of large-scale and complex systems.

We study the multichain case of a vector-valued Markov decision process with average reward criterion. We characterize optimal deterministic stationary policies via systems of linear inequalities and discuss a policy iteration algorithm for finding all optimal deterministic stationary policies.