In this paper we consider the dynamic inventory model with a discrete demand and no discounting. We verify a conjecture of Iglehart about the asymptotic behaviour of the minimal total expected cost. To do this, we give for the denumerable state dynamic programming model a number of conditions...

This paper gives an elementary proof of Iglehart's conjecture about the classical dynamic inventory model. This conjecture states that the minimal total expected cost for a planning horizon of n periods minus n times the minimal long-run average expected cost per period has a finite limit as n -...

This paper is the first part of a study of Blackwell optimal policies in Markov decision chains with a Borel state space and unbounded rewards. We prove here the existence of deterministic stationary policies which are Blackwell optimal in the class of all, in general randomized, stationary...

In this paper we will consider two-person zero-sum games and derive a general approach for solving them. We apply this approach to a queueing problem. In section 1 we will introduce the model and formulate the Key-theorem. In section 2 we develop the theory that we will use in section 3 to prove...

This paper is the second part of our study of Blackwell optimal policies in Markov decision chains with a Borel state space and unbounded rewards. We prove that a stationary policy is Blackwell optimal in the class of all history-dependent policies if it is Blackwell optimal in the class of...

In this paper we analyse a closed queueing network in which customers have to be assigned to parallel queues. The routing decision may not depend on the numbers of customers in the queues. We present an algorithm and we show that it computes an average optimal policy in case of exponential...

In this paper, we consider deterministic (both fluid and discrete) polling systems with N queues with infinite buffers and we show how to compute the best polling sequence (minimizing the average total workload). With two queues, the best polling sequence is always periodic when the system is...

This paper deals with a system where batch arrivals wait in a station until a server (a train) is available, at which moment it services all customers in waiting. This is an example of a bulk server, which has many applications in public transportation, telecommunications, computer resource...

In this paper we study a challenging call center operation problem. The goal of our analysis is to identify an optimal policy for allocating tasks to agents. As a first step, we discuss promising randomized policies and use stochastic approximation for finding the optimal randomized policy when...

Quantiles play an important role in modelling quality of service in the service industry and in modelling risk in the financial industry. Recently, Hong showed in his breakthrough papers that efficient simulation based estimators can be obtained for quantile sensitivities by means of sample path...