761 Competitive Queueing Policies for QoS Switches Nir Andelman* Yishay Mansour t An Zhu t Abstract We consider packet scheduling in a network providing differ- entiated services, where each packet is assigned a value. We study various queueing models for supporting QoS (Quality of Service). In the nonpreemptive model, packets accepted to the queue will be transmitted eventually and cannot be dropped. The FIFO preemptive model allows packets ac- cepted to the queue to be preempted (dropped) prior to their departure, while ensuring that transmitted packets are sent in the order of arrival. In the bounded delay model, packets must be transmitted before a certain deadline, otherwise it is lost (while transmission ordering is allowed to be arbitrary). In all models the goal of the buffer policy is to maximize the total value of the accepted packets. Let a be the ratio between the maximal and minimal value. For the non-preemptive model we derive a O(loga) com- petitive ratio, both exhibiting a buffer policy and a general lower bound. For the interesting case of two distinct values, we give an 2~-1 competitive buffer policy, which exactly ce matches the lower bound. We also analyze a RED-like pol- icy and derive its competitive ratio, which is approximately 2~-0.5 for two values and O(loga) for multiple values. In ct addition we improve the previous known lower and upper bounds of the Fixed Partition and Flexible Partition poli- cies. For the FIFO preemptive model, we improve the general lower bound and show a tight bound for the special case of queue size 2. We prove that the bounded delay model with uniform delay 2 is equivalent to a modified FIFO preemp- tive model with queue size 2. We then give improved upper and lower bounds on the 2-uniform bounded delay model. We also give lower bound for the 2-variable bounded delay model, which matches the previously known upper bound. 1 Introduction Currently, the Internet infrastructure provides "best ef- fort" service for all traffic streams. The uncertainty of the actual performance is not satisfactory for many --Wool of Computer Science, Tel-Aviv University, Tel-Aviv, Israel. E-mail : andeJ.mazl@cs.tau.ac,il. tSchool of Computer Science, Tel-Aviv University, Tel-Aviv, Israel. E--mail : maasottr@cs, tau. ac. il. SDepartment of Computer Science, Stanford University, Stan- ford, CA 94305. Supported by a GRPW fellowship from Bell Labs, Lucent Technologies. E-mail : emzhu@cs, staaford.edu. applications. The widely foreseen next-generation net- works will provide guaranteed services to meet various user demands. This gives rise to the recent interest in the Quality of Service (QoS) feature. This vision has been around the networking com- munity for more than a decade [15]. For instance, ATM networks serve as an example of a unified architecture that supports a diverse set of service classes. Of late, there has been termendous interest in IP in providing differentiated services via QoS guarantees. The basic methodology of QoS is rather intuitive -- commit re- sources to each admitted connection. Thus, the net- work is capable of providing different users with dif- ferent classes of service. In particular, a contract be- tween users and service providers ensures that the net- work maintains the performance guarantees provided the users stick to their commitments about traffic gen- eration. However, due to a variety of reasons, the incom- ing traffic patterns may not coincide with that speci- fied in the service contract. A typical example is that the traffic from the user does not conform to the pat- terns defined in the contract. The difficult situation is when the traffic exceeds the allocated bandwidth at some point. Another equally serious problem is that by guaranteeing the worst-case performance, the QoS network might not be efficient due to its conservative policy, as network traffic tends to be bursty. Recog- nizing this phenomenon, most modern QoS networks allow some "overbooking," employing the policy pop- ularly known as statistical multiplexing [8]. In either case, QoS networks must resolve the unavoidable issue of overloading. This paper analyzes queueing policies under overloading using competitive analysis. In the past few years the networking community has had an increasing interest in QoS networks [6, 12, 13, 14]. A major new paradigm suggested is that of assured service [5]. This service has a loose guarantee in which traffic conforming to the specified pattern is much less likely to be dropped in the network. This approach leads to two types of packets in the system: those of high priority (conformed traffic) and those of low priority (uncolfformed traffic). We can now abstract the problem as follows. We assign a value to each packet: value 1 for the low priority