We consider a multiserver delay queue with finite additional waiting spaces and time-varying arrival rates, where the customers waiting in the buffer may abandon. These are features that arise naturally from the study of service systems such as call centers. Moreover, we assume rewards for successful service completions and cost rates for service resources. Finally, we consider service-level agreements that constrain both the fractions of callers who abandon and the ones who are blocked.

Applying the theory of Lagrangian mechanics to the fluid limit of a related Markovian service network model, we obtain near-profit-optimal staffing and provisioning schedules. The nature of this solution consists of three modes of operation. A key step in deriving this solution is combining the modified offered load approximation for loss systems with our fluid model. We use them to estimate effectively both our service-level agreement metrics and the profit for the original queuing model. Second-order profit improvements are achieved through a modified offered load version of the conventional square root safety rule.

Numerous examples of real-time services arise in the service industry that can be modeled as loss systems. These include agent staffing for call centers, provisioning bandwidth for private line services, making rooms available for hotel reservations, and congestion pricing for parking spaces. Given that arriving customers make their decision to join the system based on the current service price, the manager can use price as a mechanism to control the utilization of the system. A major objective for the manager is then to find a pricing policy that maximizes total revenue while meeting the quality of service targets desired by the customers. For systems with growing demand and service capacity, we provide a dynamic pricing algorithm. A key feature of our solution is congestion pricing. We use demand forecasts to anticipate future service congestion and set the present price accordingly.

A variety of foods (peas (Pisum sativum), chicken meat, eggs, goat's milk, human milk) enriched with the stable isotope 67Zn were prepared by means of intrinsic- and extrinsic-labelling procedures. They were fed to rats and apparent absorption of 67Zn determined from faecal excretion measurements using thermal ionization mass spectrometry. There were significant differences in the absorption of the extrinsic and intrinsic label which differed in magnitude between the foods tested. The extrinsic 67Zn was less well absorbed in peas, chicken meat, eggs, and human milk than intrinsic 67Zn, but in goat's milk the extrinsic 67Zn was better absorbed than the intrinsic label. These results demonstrate that extrinsically-added stable Zn isotopes do not fully exchange with endogenous Zn in many foods, and illustrate the need for caution when using extrinsic labels for Zn bioavailability studies.