A novel algorithm for dynamic admission control of elastic flows Franco Blanchini, Daniele Casagrande and Pier Luca Montessoro Abstract—The task of assigning part of the forwarding ca- pability of a router to different flows, usually called admission control, is considered and an algorithm to handle the requests is developed. The idea is to admit not only the acceptance and the rejection answers but also a third kind of answer that occurs when there is no available share of the resource at the instant of the request but there may be a quote of resource available in a determined time-window in the future, provided that the active flows are suitably decreased. The algorithm guarantees both the fair occupancy of the resource and the optimality of its usage. Moreover, the only information on which the algorithm relies is the number of flows, and for each one, the minimum bandwidth needed and the desired bandwidth. Index terms– Bandwidth assignment, admission control, elastic flow. I. I NTRODUCTION When a resource is shared among several users, managing the allocation of the resource to the users requesting becomes a difficult task if fairness among users and the maximization of the usage are to be guaranteed. In this article we consider the task, performed by a router, of assigning part of its forwarding capability to different flows, usually called admission control, and we develop an algorithm to handle the requests. In the literature, diverse algorithms are available for admission control [1], [2], [3], [4], [5], [6]. However, to the best of these authors’ knowledge, all the available methods perform a straight rejection, i.e. either the router admits a new flow and assign to it some rate of transmission, or the request is rejected. On the contrary, the idea developed herein is to admit also a third kind of answer when there is no available share of the resource at the instant of the request but there may be a quote of resource available in a determined time-window in the future, provided that the active flows are suitably decreased. In this way a user, the request of which is unsatisfied, can decide to wait and try again after a given time-interval. The algorithm described herein guarantees both the fair occupancy of the resource and the optimality of its usage. The control works on a per-flow dynamic resource reser- vation schema, made scalable by the underlying algorithm REBOOK [7], that provides constant cost for flow table access regardless the number of active flows. Moreover, another ad- vantage of the proposed algorithm is that the only information on which it relies consists is the number of flows, and for each one, the minimum quote, namely the minimum bandwidth needed for the source to be able to deliver the service, and the desired quote, namely the bandwidth requested by the source for optimal quality level. The task of the router is modeled making use of two different discrete time scales. The first, with a smaller time period, corresponds to the time scale of the communication between the router and the end nodes; this is also the time scale of the upgrading of the flow information table. The second time scale, with a larger time period, corresponds to the action of the control law. The event of a new source requesting the use of the channel and the event of a source stopping using it are treated asynchronously with respect to the time scale of the control law and, more importantly, no assumption is made on the statistics of the requests; hence, the validity of the method is general. II. NOTATION The following notation is used throughout the article. n(t) is the total number of sources transmitting to the router at time t; l i ∈ [0, 1], i =1,...,n(t), denotes the minimum level of transmission rate of the i-th source, namely the transmission rate below which the source cannot transmit; r i ∈ [0, 1] denotes the transmission rate requested by the i-th source; obviously r i ≥ l i ; x i (t) ∈ [0,r i − l i ] is the quote, namely the amount of transmission rate at time t, associated with the i-th source, that can be assigned managed by the controller; R i (t)= x i (t)+ l i denotes the total transmission rate assigned at the instant t to the i-th source; R i (t) ∈ [l i ,r i ]; y(t) denotes the overall transmission rate at time t, that is y(t)= n(t)  i=1 R i (t) . We assume that all the quantities are normalized, namely that the capacity of the channel is 1. III. STEADY STATE In this section we describe a model for the dynamics of the manageable amounts of transmission rate x i in the simplified scenario in which no new request occur. Obviously, this is not the final purpose of this work; however, this first result is accessory for the theory that is developed in the remainder of the article. To begin with, we make the ideal assumption that all the quantities vary continuously with time and we suppose that the router can behave as a control system, namely that it can affect the time-variation of the rate of transmission assigned to each source, thus obtaining the following model: ˙ x i (t)= u i (t) , (1) 50th FITCE CONGRESS PROCEEDINGS ________________________________________________________________________________________________ ________________________________________________________________________________________________ Palermo - August 31th – September 3rd , 2011 Page 110