We study the problem of assigning @math identical servers to a set of @math parallel queues in a time-slotted queueing system. The connectivity of each queue to each server is randomly changing with time; each server can serve at most one queue and each queue can be served by at most one server during each time slot. Such a queueing model has been used in addressing resource allocation problems in wireless networks. It has been previously proven that Maximum Weighted Matching (MWM) is a throughput-optimal server assignment policy for such a queueing system. In this paper, we prove that for a system with i.i.d. Bernoulli packet arrivals and connectivities, MWM minimizes, in stochastic ordering sense, a broad range of cost functions of the queue lengths such as total queue occupancy (which implies minimization of average queueing delays). Then, we extend the model by considering imperfect services where it is assumed that the service of a scheduled packet fails randomly with a certain probability. We prove that the same policy is still optimal for the extended model. We finally show that the results are still valid for more general connectivity and arrival processes which follow conditional permutation invariant distributions.
For more information on optimal scheduling and resource allocation problems in wireless networks the reader is encouraged to also consult with @cite_7 @cite_28 @cite_14 @cite_19 @cite_21 @cite_24 .
@cite_14 @cite_7 @cite_28 @cite_21 @cite_24 @cite_19
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With an abstraction of serving rate-adaptive sources on a broadcast-type wireless channel as a utility maximization problem, it is shown how one can design many intuitive online scheduling policies based upon the feedback that one obtains at the scheduler. Using a stochastic approximation argument it is then shown that the constructed algorithms converge to optimal solutions of the utility maximization problem over different sets which critically depend on the quality of the feedback information. Information flow in a telecommunication network is accomplished through the interaction of mechanisms at various design layers with the end goal of supporting the information exchange needs of the applications. In wireless networks in particular, the different layers interact in a nontrivial manner in order to support information transfer. In this text we will present abstract models that capture the cross-layer interaction from the physical to transport layer in wireless network architectures including cellular, ad-hoc and sensor networks as well as hybrid wireless-wireline. The model allows for arbitrary network topologies as well as traffic forwarding modes, including datagrams and virtual circuits. Furthermore the time varying nature of a wireless network, due either to fading channels or to changing connectivity due to mobility, is adequately captured in our model to allow for state dependent network control policies. Quantitative performance measures that capture the quality of service requirements in these systems depending on the supported applications are discussed, including throughput maximization, energy consumption minimization, rate utility function maximization as well as general performance functionals. Cross-layer control algorithms with optimal or suboptimal performance with respect to the above measures are presented and analyzed. A detailed exposition of the related analysis and design techniques is provided. Scheduling has been extensively studied in various disciplines in operations research and wireline networking. However, the unique characteristics of wireless communication systems - namely, time-varying channel conditions and multiuser diversity - means that new scheduling solutions need to be developed that are specifically tailored for this environment. In this paper, we summarize various opportunistic scheduling schemes that exploit the time-varying nature of the radio environment to improve the spectrum efficiency while maintaining a certain level of satisfaction for each user. We also discuss the advantages and costs associated with opportunistic scheduling, and identify possible future research directions. In a preferred embodiment, a drill gas turbine motor in which the housing structure directs pressurized gas both radially inwardly and axially along the longitudinal axis of the elongated housing, against vanes arranged along a circumscribing surface of the revolvable (rotatable) rotor mounted within rotor space within the housing to effect rotation of the rotor, and a drivable shaft extending from an opening at one end of the housing, and a dampening-spring mechanism at an opposite end of the housing and rotor arranged to dampen pressure and movement of the rotor in a direction away from the end of the drivable shaft thereby reducing wear on bearings supporting the rotar at opposite ends thereof, together with brake mechanism for manually exerting braking pressure against the rotor, and key mechanism for locking the rotor in a non-revolvable state during change of chuck on the drivable shaft, and the drivable shaft having formed in a distal end thereof a female receptacle receivable of a male end of a chuck. Fair scheduling of delay and rate-sensitive packet flows over a wireless channel is not addressed effectively by most contemporary wireline fair-scheduling algorithms because of two unique characteristics of wireless media: (1) bursty channel errors and (2) location-dependent channel capacity and errors. Besides, in packet cellular networks, the base station typically performs the task of packet scheduling for both downlink and uplink flows in a cell; however, a base station has only a limited knowledge of the arrival processes of uplink flows. We propose a new model for wireless fair-scheduling based on an adaptation of fluid fair queueing (FFQ) to handle location-dependent error bursts. We describe an ideal wireless fair-scheduling algorithm which provides a packetized implementation of the fluid mode, while assuming full knowledge of the current channel conditions. For this algorithm, we derive the worst-case throughput and delay bounds. Finally, we describe a practical wireless scheduling algorithm which approximates the ideal algorithm. Through simulations, we show that the algorithm achieves the desirable properties identified in the wireless FFQ model. We consider the problem of allocating resources (time slots, frequency, power, etc.) at a base station to many competing flows, where each flow is intended for a different receiver. The channel conditions may be time-varying and different for different receivers. It is well-known that appropriately chosen queue-length based policies are throughput-optimal while other policies based on the estimation of channel statistics can be used to allocate resources fairly (such as proportional fairness) among competing users. In this paper, we show that a combination of queue-length-based scheduling at the base station and congestion control implemented either at the base station or at the end users can lead to fair resource allocation and queue-length stability.