Yechiam Yemini

An Optimal Algorithm for Scheduling Reservations in a Bandwidth Market

algorithm is presented which provides an optimal solution to the problem of scheduling non-relocatable time intervals of bandwidth in differentiated services networks. Simulations found an asymmetry between valuing an intervals length and bandwidth requirement. Longer intervals requiring less resource are favored over shorter intervals requiring more resource. The optimal algorithm is shown to respond appropriately to price as a mechanism of control whereas the offline greedy and the online FCFS algorithms do not. The solution uses integer programming, and it is shown that, except in the general case, the problem can be solved in polynomial time. A. INTRODUCTION In a differentiated services[8][9] or integrated serv-ices[16] environment, a service provider will allocate a percentage of its overall bandwidth for use in assured forwarding[18] or guaranteed service[17]. The provider provisions access to this limited resource among multiple price-competing customers. Market-based mechanisms have been successfully applied to the problem of allocation and control of resources in large distributed sys-tems[5][7]. Bandwidth markets as described in [12][3][5] are such examples. In this model, each customer requires bandwidth during a unique time interval that is fixed in time (non-relocatable) and the bandwidth requirement varies from customer to customer. As such, each interval is uniquely priced. The service provider may price each customers requirement based on amount of bandwidth required, the length of the interval, historical and current demand for the time frame, and a variety of other variables such as price competition. Orthogonal to the question of pricing, service providers must decide which customers will receive the guaranteed service. Given a limited amount of bandwidth, in the presence of previous allocations and overlapping intervals of various prices, which subset of customers should a service provider select to service in order to maximize profits? This paper gives an optimal algorithm for solving this problem. B. BANDWIDTH MARKET Consider an environment in which customers purchase bandwidth in advance for a specific time interval and transmission rate 1. Customers specify their requirements as a 4-tuple, bid = (s,e,r,p), where s is the start time of the interval, e is the end time of the interval, r is the required transmission rate and p is the price. In such a competitive environment a service provider can be queried by many comparative shoppers for the price associated for their specific intervals. Upon making their decision, some shoppers may return to the service provider to purchase the service. time Figure 1 Canonical …