In this paper, we consider a d-node GI|GI|1 tandem queue with i.i.d. inter-arrival process and service processes that are independent of each other. Our main interest is to estimate the probability to reach a high level N in a busy cycle of the system using simulation. As crude simulation does not give a sufficient precision in reasonable time, we use importance sampling. We introduce a method to find a state-independent change of measure and we show that this is equivalent to a change of measure that was earlier, but implicitly, described by Parekh and Walrand [8]. We also show that this change of measure is the only exponential state-independent change of measure that may result in an asymptotically efficient estimator. Lastly, we provide necessary conditions for this state-independent change of measure to give an asymptotically efficient estimator.

This paper introduces two statistics that assess whether (or not) a sequence sampled from a stationary time-homogeneous Markov chain on a finite state space is reversible. The test statistics are based on observed deviations of transition sample counts between each pair of states in the chain. First, the joint asymptotic normality of these sample counts is established. This result is then used to construct two chi-squared-based tests for reversibility. Simulations assess the power and type one error of the proposed tests.

We propose a generalized extreme shock model with a possibly increasing failure threshold. Although standard models assume that the crucial threshold for the system might only decrease over time, because of weakening shocks and obsolescence, we assume that, especially at the beginning of the system's life, some strengthening shocks might increase the system tolerance to large shock. This is, for example, the case of turbines’ running-in in the field of engineering. On the basis of parametric assumptions, we provide theoretical results and derive some exact and asymptotic univariate and multivariate distributions for the model. In the last part of the article we show how to link this new model to some nonparametric approaches proposed in the literature.

We study call admission rates in a linear communication network with each call identified by an arrival time, duration, bandwidth requirement, and origin-destination pair. Network links all have the same bandwidth capacity, and a call can be admitted only if there is sufficient bandwidth available on every link along the call's path. Calls not admitted are held in a queue, in contrast to the protocol of loss networks. We determine maximum admission rates (capacities) under greedy call allocation rules such as First Fit and Best Fit for several baseline models and prove that the natural necessary condition for stability is sufficient. We establish the close connections between our new problems and the classic problems of bin packing and interval packing. In view of these connections, it is surprising to find that Best Fit allocation policies are inferior to First Fit policies in the models studied.

We give an extremely simple argument to prove that in infinite user-commurlication channels, under the Aloha protocol, the number of successful transmissions is finite with probability 1. The same result is then shown to hold for those back-off protocols whose transmission probabilities are bounded away from 0.

We consider a renewal reward process in continuous time. The supremum average reward, γ* for this process can be characterised as the unique root of a certain function. We show how one can apply the Newton–Raphson algorithm to obtain successive approximations to γ*, and show that the successive approximations so obtained are the same as those obtained by using the policy improvement technique.

We analyze a continuous review inventory model with the marginal carrying cost of a unit of inventory given by an increasing function of its shelf age and the marginal delay cost of a backlogged demand unit by an increasing function of its delay duration. We show that, under a minor restriction, an (r, q)-policy is optimal when the demand process is a renewal process, and a state dependent (r, q)-policy is optimal when the demand is a Markov-modulated renewal process. We also derive various monotonicity properties for the optimal policy parameters r* and r* + q*.

In the subject of optimal stopping, the classical secretary problem is concerned with optimally selecting the best of n candidates when their relative ranks are observed sequentially. This problem has been extended to optimally selecting the kth best candidate for k ≥ 2. While the optimal stopping rule for k=1,2 (and all n ≥ 2) is known to be of threshold type (involving one threshold), we solve the case k=3 (and all n ≥ 3) by deriving an explicit optimal stopping rule that involves two thresholds. We also prove several inequalities for p(k, n), the maximum probability of selecting the k-th best of n candidates. It is shown that (i) p(1, n) = p(n, n) > p(k, n) for 1<k<n, (ii) p(k, n) ≥ p(k, n + 1), (iii) p(k, n) ≥ p(k + 1, n + 1) and (iv) p(k, ∞): = lim n→∞p(k, n) is decreasing in k.

This paper extends product form results for queueing networks with signals to allow history-dependent routing. The signals in these models carry information to nodes and induce multiple customers to move simultaneously within the network. Two models are studied in this paper. In the first one we assume that routing probabilities of a departing customer from a given class of nodes depend on the amount of service just received by the customer and whether its departure is the result of an actual service completion or the result of an arriving signal. In the second model we assume that the routing probabilities of a customer depend on the number of times this customer's service has been interrupted by signals in the past as well as the cause of its departure. We show that both models possess simple product form solutions. These results provide a new dimension in modeling and analyzing practical systems.

The line reversibility property of a two-stage multiserver system with manufacturing blocking has previously been established using a duality argument between the blocked state and the idle state. In this paper, we provide counterexamples that show this argument does not apply to systems with more than two stages. A focus of this paper is to provide a new proof for the result. Our argument is based on the duality between the service initiation and the service completion events.

Relying only on the classical Bahadur–Rao approximation for large deviations (LDs) of univariate sample means, we derive strong LD approximations for probabilities involving two sets of sample means. The main result concerns the exact asymptotics (as n→∞) of

$$ {\open P}\left({\max_{i\in\{1,\ldots,d_x\}}\bar X_{i,n} \les \min_{i\in\{1,\ldots,d_y\}}\bar Y_{i,n}}\right),$$

${\bar X}_{i,n}{\rm s}$

${\bar Y}_{i,n}{\rm s}$

${\open E}X \gt {\open E}Y$

We consider preemptive and nonpreemptive scheduling of partially ordered tasks on parallel processors, where the precedence relations have an intervalorder, an in-forest, or a uniform out-forest structure. Processing times of tasks are random variables with an increasing in likelihood ratio distribution in the nonpreemptive case and an exponential distribution in the preemptive case. We consider a general cost that is a function of time and of the uncompleted tasks and show that the most successors (MS) policy stochastically minimizes the cost function when it satisfies certain agreeability conditions. A consequence is that the MS policy stochastically minimizes makespan, weighted flowtime, and the weighted number of late jobs.

We consider a simple model of sequential decisions made by a fusion agent that receives binary-passive reports from distributed sensors. The main result is an explicit formula for the probability of making a decision before a fixed budget is exhausted. These results depend on the relationship between a special ruin problem for a “lazy random walk” and a traditional biased walk.

We consider a two-echelon production inventory system with a manufacturer having limited production capacity and a distribution center (DC). There is a positive transportation time between the manufacturer and the DC. Customers gain a value by receiving the product and incur a waiting cost when facing a delay. We assume that customers' waiting cost depends on their degree of impatience with respect to delay, which is captured by a convex waiting cost function. Customers are strategic with respect to joining the system and either place an order or balk from the system upon their arrival depending on their expected waiting time. We study the Stackelberg equilibrium assuming that the DC acts as a Stackelberg leader and customers are the followers. We first obtain the total expected revenue and then provide a heuristic to derive the optimal base-stock levels in the warehouse and the DC as well as the optimal price of the product.

We consider the problem of estimation of the standard deviation σ and the process capability indices Cp and Cpm for a normally distributed process. The problem is addressed with the objective of obtaining optimal estimators under the classic criterion of minimum variance unbiased estimation, as well as under the Pitman measure of closeness.

We analyze the asymptotic number of items chosen in a selection procedure. The procedure selects items whose rank among all previous applicants is within the best 100p percent of the number of previously selected items. We use analytic methods to obtain a succinct formula for the first-order asymptotic growth of the expected number of items chosen by the procedure.

One of the interesting problems on the stochastic behavior of random recurrent events in a random time interval is to obtain the conditions under which the reliability properties of a random time T are inherited by N(T), where {N(t):t≥0} is a stochastic process. Most of the studies on the topic has been done under the assumption that the random time T and the stochastic process {N(t):t≥0} are stochastically independent. However, in practice, there can be different cases when appropriate dependence structure is more appropriate. In this paper, we study the preservation of a renewal process stopped at a random time when they are “stochastically dependent.” We discuss the stochastic ordering properties and the preservation of reliability classes for the random counting variables N(T) when the corresponding counting process is a renewal process. Furthermore, we study the preservation of NBUE (NWUE) reliability class when the counting process is a homogeneous Poisson process.

In this paper, we develop a novel game theoretic model of the interactions between an EDoS attacker and the defender based on a signaling game that is a dynamic game of incomplete information. We then derive the best defense strategies for the network defender to respond to the EDoS attacks. That is, we compute the perfect Bayesian Nash Equilibrium (PBE) of the proposed game model such as the pooling PBE, separating PBE and mixed strategy PBE. In the pooling equilibrium, each type of the attacker takes the same action and the attacker's type is not revealed to the defender, whereas in the separating equilibrium, each type of the attacker uses different actions and hence the attacker's type is completely revealed to the defender. On the other hand, in the mixed strategy PBE, both the attacker and the defender randomize their strategies to optimize their payoffs. Numerical illustration is also presented to show the efficacy of the proposed model.

In this paper, the classical compound Poisson model under periodic observation is studied. Different from the random observation assumption widely used in the literature, we suppose that the inter-observation time is a constant. In this model, both the finite-time and infinite-time Gerber-Shiu functions are studied via the Laguerre series expansion method. We show that the expansion coefficients can be recursively determined and also analyze the approximation errors in detail. Numerical results for several claim size density functions are given to demonstrate effectiveness of our method, and the effect of some parameters is also studied.

In this paper, we study the problem of dynamic allocation of a single server to parallel queues with finite-capacity buffers. The arrival processes are mutually independent, equal rate Poisson processes, and the service times are independent and identically distributed random variables with an arbitrary distribution. We are interested in characterizing the allocation policy that stochastically minimizes the number of customers lost due to buffer overflows. Using a coupling argument, we establish the optimality of the Fewest-Empty-Spaces policy, which allocates the server to the queue with the fewest empty buffer spaces, within the class of nonpreemptive and nonidling policies. The result extends to the class of preemptive policies, if the service times are exponentially distributed. We also briefly discuss the allocation problem under more general statistical assumptions on the arrival processes.