Responding to unexpected overloads in large-scale service systems

We consider how two networked large-scale service systems that normally operate separately, such as call centers, can help each other when one encounters an unexpected overload and is unable to immediately increase its own staffing. Our proposed control activates serving some customers from the other system when a ratio of the two queue lengths (numbers of waiting customers) exceeds a threshold. Two thresholds, one for each direction of sharing, automatically detect the overload condition and prevent undesired sharing under normal loads. After a threshold has been exceeded, the control aims to keep the ratio of the two queue lengths at a specified value. To gain insight, we introduce an idealized stochastic model with two customer classes and two associated service pools containing large numbers of agents. To set the important queue-ratio parameters, we consider an approximating deterministic fluid model. We determine queue-ratio parameters that minimize convex costs for this fluid model. We perform simulation experiments to show that the control is effective for the original stochastic model. Indeed, the simulations show that the proposed queue-ratio control with thresholds outperforms the optimal fixed partition of the servers given known fixed arrival rates during the overload, even though the proposed control does not use information about the arrival rates.