A multi-class deterministic fluid model is proposed to describe and improve the performance of a customer contact center with skill-based routing. The fluid model can be regarded as an approximation for a stochastic queueing system with multiple customer classes and multiple server groups, with customer abandonment and non-exponential service-time and time-to-abandon distributions. The fluid mo...

We consider queueing systems in which customers arrive according to a Poisson process and have exponentially distributed service requirements. The customers are impatient and may abandon the system while waiting for service after a generally distributed amount of time. The system incurs customer-related costs that consist of waiting and abandonment penalty costs. We study capacity sizing in suc...

Determining the optimal location of facilities to serve a spatially disnersed set of customers has been an increasingly active research area during the past twenty years. Many systems whose facilities are to be located operate in a stochastic environment, with uncertainties associated with the arrival time, location and service requirements of each customer. Facilities having finite service cap...

We propose a dynamically consistent framework that allows joint valuation and estimation of stock options and credit default swaps written on the same reference company. We model default as controlled by a Poisson process with a stochastic default arrival rate. When default occurs, the stock price drops to zero. Prior to default, the stock price follows a continuous process with stochastic vola...

We consider the asymptotic variance of the departure counting processD(t) of the GI/G/1 queue;D(t) denotes the number of departures up to time t. We focus on the case that the system load % equals 1, and prove that the asymptotic variance rate satisfies lim t→∞ VarD(t) t = λ ( 1− 2 π )( ca + c 2 s ) , where λ is the arrival rate and ca, cs are squared coefficients of variation of the inter-arri...

We study a batch arrival M/M/1 queue with multiple working vacation. The server serves customers at a lower rate rather than completely stopping service during the service period. Using a quasi upper triangular transition probability matrix of two-dimensional Markov chain and matrix analytic method, the probability generating function (PGF) of the stationary system length distribution is obtain...