Management of online server congestion using optimal demand throttling

Bandwidth throttling is widely employed in practice by online-service-providers (OSPs) as a server/network congestion management tool. However, this topic has been largely neglected in the academic literature. To the best of our knowledge, this is the first analytical study that aims at achieving an optimal (non-discriminatory) throttling mechanism for bandwidth when user demand is stochastic. In our setting, the demand dynamics of the OSP is governed by a geometric Brownian process. There are costs associated with maintaining and throttling demand; in particular, throttling cost includes both fixed and proportional costs. As users experience inferior service speeds during throttling, the proposed model modifies the demand dynamics to adequately capture users’ reactions to throttling. OSP's objective is to determine the optimal throttling strategy that minimizes the total expected discounted cost of maintaining and throttling demand. By assuming the existence of an optimal strategy, we use a dynamic programming (Quasi-Variational Inequality) approach to show that it is optimal for the OSP to throttle the demand whenever it reaches a threshold level and downgrade the service speed by a fixed factor while the throttling is employed. Our numerical computations strongly suggest that it is always optimal for OSPs to induce negative (demand) growth rates during throttling to reduce unfavorable future demand. Moreover, our comparative statics analysis explains how OSPs should handle user demand with higher growth rates and volatility, service networks that face higher demand fluctuations/volatility during throttling, and the trade-off between non-monetary fixed and proportional cost associated with throttling.