Stochastic Systems ACHIEVING RAPID RECOVERY IN AN OVERLOAD CONTROL FOR LARGE-SCALE SERVICE SYSTEMS

We consider an automatic overload control for two large service systems modeled as multi-server queues, such as call centers. We assume that the two systems are designed to operate independently, but want to help each other respond to unexpected overloads. The proposed overload control automatically activates sharing (sending some customers from one system to the other) once a ratio of the queue lengths in the two systems crosses an activation threshold (with ratio and activation threshold parameters for each direction). To prevent harmful sharing, sharing is allowed in only one direction at any time. In this paper, we are primarily concerned with ensuring that the system recovers rapidly after the overload is over, either (i) because the two systems return to normal loading or (ii) because the direction of the overload suddenly shifts in the opposite direction. To achieve rapid recovery, we introduce lower thresholds for the queue ratios, below which one-way sharing is released. As a basis for studyin

A simulation of a police patrol service system with multi-grade time-varying incident arrivals

Due to the squeeze on public expenditure, the funding cuts imposed on the police provide a great impetus to find an efficient incident response sequence with limited resources. This is especially the case for police response systems which exhibit the characteristics of time-varying volume of demand. In this paper, we investigate two types of priority queues in the patrol service system. Both the incident arrival rate and the scheduled staff level change with time. For such a system, there is no analytical model available to give close-form performance, so simulation is used for the study. Although dynamic priority queues which enable more flexibility in setting the sequence of service requests are widely applied in many service systems, such as the NHS service system, the simulation model results show that in police patrol service systems static priority queue performs better

A Switching Fluid Limit of a Stochastic Network Under a State-Space-Collapse Inducing Control with Chattering

Routing mechanisms for stochastic networks are often designed to produce state space collapse (SSC) in a heavy-traffic limit, i.e., to confine the limiting process to a lower-dimensional subset of its full state space. In a fluid limit, a control producing asymptotic SSC corresponds to an ideal sliding mode control that forces the fluid trajectories to a lower-dimensional sliding manifold. Within deterministic dynamical systems theory, it is well known that sliding-mode controls can cause the system to chatter back and forth along the sliding manifold due to delays in activation of the control. For the prelimit stochastic system, chattering implies fluid-scaled fluctuations that are larger than typical stochastic fluctuations. In this paper we show that chattering can occur in the fluid limit of a controlled stochastic network when inappropriate control parameters are used. The model has two large service pools operating under the fixed-queue-ratio with activation and release thresholds (FQR-ART) overload control which we proposed in a recent paper. We now show that, if the control parameters are not chosen properly, then delays in activating and releasing the control can cause chattering with large oscillations in the fluid limit. In turn, these fluid-scaled fluctuations lead to severe congestion, even when the arrival rates are smaller than the potential total service rate in the system, a phenomenon referred to as congestion collapse. We show that the fluid limit can be a bi-stable switching system possessing a unique nontrivial periodic equilibrium, in addition to a unique stationary point

Achieving rapid recovery in an overload control for large-scale service systems. Working paper, Columbia University. Available at: http://www.columbia.edu/∼ww2040/allpapers.html

W e consider an automatic overload control for two large service systems modeled as multiserver queues such as call centers. We assume that the two systems are designed to operate independently, but want to help each other respond to unexpected overloads. The proposed overload control automatically activates sharing (sending some customers from one system to the other) once a ratio of the queue lengths in the two systems crosses an activation threshold (with ratio and activation threshold parameters for each direction). In this paper, we are primarily concerned with ensuring that the system recovers rapidly after the overload is over, either because (i) the two systems return to normal loading or (ii) the direction of the overload suddenly shifts in the opposite direction. To achieve rapid recovery, we introduce lower thresholds for the queue ratios, below which one-way sharing is released. As a basis for studying the complex dynamics, we develop a new six-dimensional fluid approximation for a system with time-varying arrival rates, extending a previous fluid approximation involving a stochastic averaging principle. We conduct simulations to confirm that the new algorithm is effective for predicting the system performance and choosing effective control parameters. The simulation and the algorithm show that the system can experience an inefficient nearly periodic behavior, corresponding to an oscillating equilibrium (congestion collapse) if the sharing is strongly inefficient and the control parameters are set inappropriately