This paper analyzes a call center model with m customer classes and r agent pools. The model is one with doubly stochastic arrivals, which means that the m-vector of instantaneous arrival rates is allowed to vary both temporally and stochastically. Two levels of call center management are considered: staffing the r pools of agents, and dynamically routing calls to agents. The system manager's objective is to minimize the sum of personnel costs and abandonment penalties. We consider a limiting parameter regime that is natural for call centers and relatively easy to analyze, but apparently novel in the literature of applied probability. For that parameter regime, we prove an asymptotic lower bound on expected total cost, which uses a strikingly simple distillation of the original system data. We then propose a method for staffing and routing based on linear programming (LP), and show that it achieves the asymptotic lower bound on expected total cost; in that sense the proposed method is asymptotically optimal.

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We consider the risk of a portfolio comprised of loans, bonds, and financial instruments that are subject to possible default. In particular, we are interested in performance measures such as the probability that the portfolio incurs large losses over a fixed time horizon and the expected excess loss given that large losses are incurred during this horizon. Contrary to the normal copula that is commonly used in practice (e.g., in the CreditMetrics system), we assume a portfolio dependence structure that is semiparametric, does not hinge solely on correlation, and supports extremal dependence among obligors. A particular instance within the proposed class of models is the so-called t-copula model that is derived from the multivariate Student t distribution and hence generalizes the normal copula model. The size of the portfolio, the heterogenous mix of obligors, and the fact that default events are rare and mutually dependent makes it quite complicated to calculate portfolio credit risk either by means of exact analysis or naïve Monte Carlo simulation. The main contributions of this paper are twofold. We first derive sharp asymptotics for portfolio credit risk that illustrate the implications of extremal dependence among obligors. Using this as a stepping stone, we develop importance sampling algorithms that are shown to be asymptotically optimal and can be used to efficiently compute portfolio credit risk via Monte Carlo simulation.

Delay announcements informing customers about anticipated service delays are prevalent in service-oriented systems.How delay announcements can influence customers in service systems is a complex problem which depends on both the dynamics of the underlying queueing system and on the customers' strategic behavior. We examine this problem of information communication by considering a model in which both the firm and the customers act strategically: the firm in choosing its delay announcement while anticipating customer response, and the customers in interpreting these announcements and in making the decision about when to join the system and when to balk. We characterize the equilibrium language that emerges between the service provider and her customers. The analysis of the emerging equilibria provides new and interesting insights into customer-firm information sharing. We show that even though the information provided to customers is non-verifiable, it improves the profits of the firm and the expected utility of the customers. The robustness of the results is illustrated via various extensions of the model. In particular, studying models with incomplete information on the system parameters and multiple customer types allows us also to highlight the role of information provision in managing customer expectations regarding the congestion in the system. Further, the information could be as simple as "High Congestion"/"Low Congestion" announcements, or could be as detailed as the true state of the system.We also show that firms may choose to shade some of the truth by using intentional vagueness to lure customers.*