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We consider the following queuing system which arises as a model of a wireless link shared by multiple users+ There is a finite number N of input flows served by a server+ The system operates in discrete time t ϭ 0,1,2, + + + + Each input flow can be described as an irreducible countable Markov chain; waiting customers of each flow are placed in a queue+ The sequence of server states m~t !, t ϭ 0,1,2, + + + , is a Markov chain with finite number of states M+ When the server is in state m, it can serve µ i m customers of flow i~in one time slot!+ The scheduling discipline is a rule that in each time slot chooses the flow to serve based on the server state and the state of the queues+ Our main result is that a simple online scheduling discipline, Modified Largest Weighted Delay First, along with its generalizations, is throughput optimal; namely, it ensures that the queues are stable as long as the vector of average arrival rates is within the system maximum stability region+

We consider the problem of scheduling bursts of data in an optical network with an ultrafast tunable laser and a fixed receiver at each node. Due to the high data rates employed on the optical links, the burst transmissions typically last for very short times compared with the round trip propagation times between source-destination pairs. A good schedule should ensure that 1) there are no transmit/receive conflicts; 2) propagation delays are observed; and 3) throughput is maximized (schedule length is minimized). We formulate the scheduling problem with periodic demand as a generalization of the well-known crossbar switch scheduling. We prove that even in the presence of propagation delays, there exist a class of computationally viable scheduling algorithms which asymptotically achieve the maximum throughput obtainable without propagation delays. We also show that any schedule can be rearranged to achieve a factor-two approximation of the maximum throughput even without asymptotic limits. However, the delay/throughput performance of these schedules is limited in practice. We consequently propose a scheduling algorithm that exhibits near optimal (on average within 7% of optimum) delay/throughput performance in realistic network examples.

Uplink scheduling in wireless systems is gaining importance due to arising uplink intensive data services (ftp, image uploads etc.), which could be hampered by the currently in-built asymmetry in favor of the downlink. In this work, we propose and study algorithms for efficient uplink packet-data scheduling in a CDMA cell. The algorithms attempt to maximize system throughput under transmit power limitations on the mobiles assuming instantaneous knowledge of user queues and channels. However no channel statistics or traffic characterization is necessary. Apart from increasing throughput, the algorithms also improve fairness of service among users, hence reducing chances of buffer overflows for poorly located users.The major observation arising from our analysis is that it is advantageous on the uplink to schedule "strong" users one-at-a-time, and "weak" users in larger groups. This contrasts with the downlink where one-at-a-time transmission for all users has shown to be the preferred mode in much previous work. Based on the optimal schedules, we propose less complex and more practical approximate methods, both of which offer significant performance improvement compared to one-at-a-time transmission, and the widely acclaimed Proportional Fair (PF) algorithm, in simulations. When queue content cannot be fed back, we propose a simple modification of PF, Uplink PF (UPF), that offers similar improvement.

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