Pigouvian Tolls and Welfare Optimality with Parallel Servers and Heterogeneous Customers

Congestion externalities are a well-known phenomenon in transportation and communication networks, healthcare etc. Optimization by self-interested agents in such settings typically results in equilibria which are sub-optimal for social welfare. Pigouvian taxes or tolls, which impose a user charge equal to the negative externality caused by the marginal user to other users, are a mechanism for combating this problem. In this paper, we study a non-atomic congestion game in which heterogeneous agents choose amongst a finite set of heterogeneous servers. The delay at a server is an increasing function of its load. Agents differ in their sensitivity to delay. We show that, while selfish optimisation by agents is sub-optimal for social welfare, imposing admission charges at the servers equal to the Pigouvian tax causes the user equilibrium to maximize social welfare. In addition, we characterize the structure of welfare optimal and of equilibrium allocations.

Estimation of the Optimal Threshold Policy in a Queue with Heterogeneous Servers Using a Heuristic Solution and Artificial Neural Networks

This paper deals with heterogeneous queues where servers differ not only in service rates but also in operating costs. The classical optimisation problem in queueing systems with heterogeneous servers consists in the optimal allocation of customers between the servers with the aim to minimise the long-run average costs of the system per unit of time. As it is known, under some assumptions the optimal allocation policy for this system is of threshold type, i.e., the policy depends on the queue length and the state of faster servers. The optimal thresholds can be calculated using a Markov decision process by implementing the policy-iteration algorithm. This algorithm may have certain limitations on obtaining a result for the entire range of system parameter values. However, the available data sets for evaluated optimal threshold levels and values of system parameters can be used to provide estimations for optimal thresholds through artificial neural networks. The obtained results are accompanied by a simple heuristic solution. Numerical examples illustrate the quality of estimations.

Scalable Load Balancing in the Presence of Heterogeneous Servers

In large-scale computer systems, deciding how to dispatch arriving jobs to servers is a primary factor affecting system performance. Consequently, there is a wealth of literature on designing, analyzing, and evaluating the performance of load balancing policies. For analytical tractability, most existing work on dispatching in large-scale systems makes a key assumption: that the servers are homogeneous, meaning that they all have the same speeds, capabilities, and available resources. But this assumption is not accurate in practice. Modern computer systems are instead heterogeneous: server farms may consist of multiple generations of hardware, servers with varied resources, or even virtual machines running in a cloud environment. Given the ubiquity of heterogeneity in today's systems, it is critically important to develop load balancing policies that perform well in heterogeneous environments. In this paper, we focus on systems in which server speeds are heterogeneous.