We model a single-hop mobile network under centralized control with N service classes as a system of N weighted cost parallel queues with M (1 ≤ M < N) servers, arrivals, varying binary connectivity, and Bernoulli service success at each queue. We consider scheduling problems in this system and, under various assumptions on arrivals and connectivity, derive conditions sufficient, but not necessary, to guarantee the optimality of an index policy.

Results and conditions which quantify the decrease in dependence with lag for a stationary Markov process and enable one to compare the dependence for two stationary Markov processes are obtained. The notions of dependence used in this article are the supermodular ordering and the concordance ordering. Both discrete-time and continuous-time Markov processes are considered. Some applications of the main results are given. In queueing theory, the monotonicity results of the waiting time of the nth customer as well as the stationary waiting time in an MR/GI/1 queue and the stationary workload in a Markov-modulated queue are established, thus strengthening previous results while simplifying their derivation. This article is a continuation of those by Fang et al. [7] and Hu and Joe [10].

We show that if the payoff of a European option is a convex function of the prices of the security at a fixed set of times, then the geometric Brownian motion risk neutral option price is increasing in the volatility of the security. We also give efficient simulation procedures for determining the no-arbitrage prices of European barrier, Asian, and lookback options.

Achieving high throughput in input-queued switches has been found to be difficult, especially when traffic is nonuniform in the sense that different inputs have very different cell generation rates. We show that for general arrival processes, 100% throughput can be achieved with a simple algorithm that is very easy to implement.

We consider a switch in which in each time slot, at most one cell may be transmitted from each input, and at most one cell may be received at each output. Cells that are destined for output j arrive at input i according to a stationary and ergodic process, and arrivals are queued at the input. The problem is to decide which inputs are to transmit to which outputs in each time slot in order to maximize throughput. Necessary conditions for stability are that the total arrival rate to each input must be less than 1, and the total arrival rate destined to each output must be less than 1. We propose a simple scheduling algorithm and show that with this algorithm the necessary conditions for stability are also sufficient.

Single-server queueing systems with mixed traffic are a flexible modeling tool that have been used to analyze polling systems and database striping strategies. They also have applications in manufacturing and telecommunication systems. Ordinary (open) customers arrive according to a Poisson process, receive service, and leave the system. Permanent (closed) customers remain in the system, reentering the queue after receiving service. This work examines the transient behavior of the permanent customers. The cycle times and output/departure process for the permanent customers are described.

In this article, we identify conditions under which the epoch times and the interepoch intervals of a nonhomogeneous Poisson process have logconcave densities. The results are extended to relevation counting processes. We also study discrete-time counting processes and find conditions under which the epoch times and the interepoch intervals of these discrete-time processes have logconcave discrete probability densities. The results are interpreted in terms of minimal repair and record values. Several examples illustrate the theory.

We consider all-terminal reliability, one of the more popular models in the field of network reliability. A graph with n nodes and e edges, where the nodes are perfectly reliable and the edges survive independently with equal probability p, is said to be a uniformly optimally reliable graph if it has for all values of p (0 ≤ p ≤ 1) an equal or higher reliability among all graphs with the same number of nodes and edges. Boesch et al. [4] verified the existence of uniformly optimally reliable graphs for e = n − 1, e = n, e = n + 1, and e = n + 2; he has also given a conjecture for e = n + 3. Wang [8] proved this conjecture. In this article, we present four new infinite families of graphs that we conjecture to be uniformly optimal.

In this note, we correct an error in the paper by Fu and Hu [1] for the perturbation analysis estimator given for the gradient of an American call option payoff on an underlying asset paying multiple dividends. We then introduce a different asset price model that is more straightforward than the previous model, and derive the corresponding gradient estimators. We conclude with a brief discussion of extensions of the estimator to other American-style options.

Numerical inversion of a one-sided z transform, corresponding to causal positive sequence, is considered. The numerical inversion requires the availability of a finite number of the transform's derivatives. The approximate analytical form is obtained by resorting to the maximum entropy principle. Entropy and then L1-norm convergence are proved.

In the proof of Theorem 2.6 in [1], we reduced the comparison of Ii(n) and Ii+1(n) to Ii−k(n − k) and Ii+1(n − k). Then, we mistakenly stated: “Suppose i − k > k, then we repeat the same reduction.” In fact, the reduction can be repeated only if i′ = n − k − i = i − k + 1. Consequently, Theorem 2.6 was proved only for t = 2. For similar reasons, Corollary 2.7 was proved only for t = 2, and Theorem 2.8 only for t = 1.