The revenue management literature for queues typically assumes that providers know the distribution of customer demand attributes. We study an observable1 queue that serves an unknown proportion of patient and impatient customers. The provider has a Bernoulli prior on this proportion, corresponding to an optimistic or pessimistic scenario. For every queue length, she chooses a low or a high...

Abstractions are a useful tool for computing policies in large domains modeled as a Markov Decision Process. Prior work in this field is mostly focused on developing different notions for state abstractions. In this paper, we develop a novel framework for abstractions, which unifies prior work and directly exploits symmetry at the state-action pair level, thereby uncovering a much larger number...

This paper is concerned with the problem of production planning in a stochastic manufacturing system with serial machines that are subject to breakdown and repair. The machine capacities are modeled by a Markov chain. The objective is to choose the input rates at the various machines over time in order to meet the demand for the system’s production at the minimum long-run average cost of produc...

This paper treats a discrete-time finite buffer batch arrival queue with a single working vacation and partial batch rejection in which the inter-arrival and service times are, respectively, arbitrary and geometrically distributed. The queue is analyzed by using the supplementary variable and the imbedded Markov-chain techniques. We obtain steady-state system length distributions at prearrival,...

In this paper, we focus on queues with a superposition of periodic and bursty sources where the initial states of the sources are randomly and independently selected. The dynamics of the queue are described as a reducible Markov chain. For such queues, we consider the tail probability of the queue length as the performance measure and try to estimate it by simulations. To do simulation efficien...

This paper proposes the use of discrete stochastic approximation (DSA) algorithm for a crosslayer adaptive modulation problem in wireless communications. In this system, the throughput in the physical (PHY) layer and quality of service (QoS) incurred by the queueing effects in the data link layer are required to be optimized simultaneously and in the long run. By assuming Markov decision proces...

A class of discrete time GI/D/k systems is considered for which the interarrival times have finite support and customers are served in first-in first-out FIFO order. The system is formulated as a single server queue with new general independent interarrival times and constant service duration by assuming cyclic assignment of customers to the identical servers. Then the queue length is set up as...

An analytic a priori error bound is provided for comparing performance measures of discrete time queues with those of a processor sharing queue for which steady state results can be easily obtained. The error bound is of the same order as the length of the discrete time slot. This bound is applied to derive error bounds for performance measures of a time-sharing queue approximated by a processo...