We consider a markovian multiserver queue with a finite waiting line in which a customer may decide to leave and give up service if its waiting time in queue exceeds its random deadline. We focus on the performance measure in terms of the probability of being served under both transient and stationary regimes. We investigate monotonicity properties of first and second order of this performance with respect to the buffer size, say k. Under the stationary regime, we prove that our service level is strictly increasing and concave in k, whereas we prove under the transient regime that it is only increasing in k.

This article deals with the effect of information and uncertainty on profits in an unobservable single-server queuing system. We consider scenarios in which the service rate, the service quality, or the waiting conditions are random variables that are known to the server but not to the customers. We ask whether the server is motivated to reveal these parameters. We investigate the structure of the profit function and its sensitivity to the variance of the random variable. We consider and compare variations of the model according to whether the server can modify the service price after observing the realization of the random variable.

This article provides series expansions of the stationary distribution of a finite Markov chain. This leads to an efficient numerical algorithm for computing the stationary distribution of a finite Markov chain. Numerical examples are given to illustrate the performance of the algorithm.

The concept of generalized order statistics was introduced as a unified approach to a variety of models of ordered random variables. The purpose of this article is to establish the usual stochastic and the likelihood ratio orderings of conditional distributions of generalized order statistics from one sample or two samples, strengthening and generalizing the main results in Khaledi and Shaked [15], and Li and Zhao [17]. Some applications of the main results are also given.

We study weighted path lengths (depths) and distances for increasing tree families. For those subclasses of increasing tree families, which can be constructed via an insertion process (e.g., recursive trees, plane-oriented recursive trees, and binary increasing trees), we can determine the limiting distribution that can be characterized as a generalized Dickman's infinitely divisible distribution.

Suppose that there are n types of coupons and that each new coupon collected is type i with probability pi. Suppose, further, that there are m subsets of coupon types and that coupons are collected until all of the types of at least one of these subsets have been collected. When these subsets have no overlap, we derive expressions for the mean and variance of the number of coupons that are needed. In the general case where the subsets can overlap, we derive the mean of the number that are needed. We also note that this number is an increasing failure rate on average random variable and we present a conjecture as to a sufficient condition for it to be an increasing failure rate random variable.

This article investigates reliability properties of a flexible extended linear failure-rate family of distributions generated using the relation F¯(x) = αF¯0(x)/[1 − α¯F¯0(x)], where α > 0, α¯ = 1 − α, and F¯0(x) is the reliability function of the linear failure-rate distribution.

Viterbi training (VT) provides a fast but inconsistent estimator of hidden Markov models (HMM). The inconsistency is alleviated with a little extra computation when we enable VT to asymptotically fix the true values of the parameters. This relies on infinite Viterbi alignments and associated with them limiting probability distributions. First in a sequel, this article is a proof of concept; it focuses on mixture models, an important but special case of HMM where the limiting distributions can be calculated exactly. A simulated Gaussian mixture shows that our central algorithm (VA1) can significantly improve the accuracy of VT with little extra cost. Next in the sequel, we present elsewhere a theory of the adjusted VT for the general HMMs, where the limiting distributions are more challenging to find. Here, we also present another, more advanced correction to VT and verify its fast convergence and high accuracy; its computational feasibility requires additional investigation.

We study the stochastic optimal control for an assemble-to-order system with multiple products and components that arrive at the system in random batches and according to renewal reward processes. Our purpose is to maximize expected infinite-horizon discounted profit by selecting product prices, component production rates, and a dynamic sequencing rule for assembly. We refine the solution of some static planning problem and a discrete review policy to batch arrival environment and develop an asymptotically optimal policy for the system operating under heavy traffic, which indicates that the system can be approximated by a diffusion process and exhibits a state space collapse property.