Measurement scheduling for recursive team estimation

We consider a decentralized LQG measurement scheduling problem in which every measurement is costly, no communication between observers is permitted, and the observers' estimation errors are coupled quadratically. This setup, motivated by considerations from organization theory, models measurement scheduling problems in which cost, bandwidth, or security constraints necessitate that estimates be decentralized, although their errors are coupled. We show that, unlike the centralized case, in the decentralized case the problem of optimizing the time integral of the measurement cost and the quadratic estimation error is fundamentally stochastic, and we characterize the -optimal open-loop schedules as chattering solutions of a deterministic Lagrange optimal control problem. Using a numerical example, we describe also how this deterministic optimal control problem can be solved by nonlinear programming.This research was supported in part by ARPA Grant N00174-91-C-0116 and NSF Grant NCR-92-04419.     

Multirate multicast service provisioning II: a tâtonnement process for rate allocation

In multirate multicast different users in the same multicast group can receive services at different rates depending on their own requirements and the congestion level of the network. In this two-part paper we present a general framework for addressing the optimal rate control problem in multirate multicast where the objective is the maximization of a social welfare function expressed by the sum of the users’ utility functions. In Part II we present a market based mechanism and an adjustment process that have the following features. They satisfy the informational constraints imposed by the nature of multirate multicast; and when they are combined with the results of Part I they result in an optimal solution of the corresponding centralized multirate multicast problem.     

Time-average and asymptotically optimal flow control policies in networks with multiple transmitters

We considerM transmitting stations sending packets to a single receiver over a slotted time-multiplexed link. For each phase consisting ofT consecutive slots, the receiver dynamically allocates these slots among theM transmitters. Our objective is to characterize policies that minimize the long-term average of the total number of messages awaiting service at theM transmitters. We establish necessary and sufficient conditions on the arrival processes at the transmitters for the existence of finite cost time-average policies; it is not enough that the average arrival rate is strictly less than the slot capacity. We construct a pure strategy that attains a finite average cost under these conditions. This in turn leads to the existence of an optimal time-average pure policy for each phase lengthT, and to upper and lower bounds on the cost this policy achieves. Furthermore, we show that such an optimal time-average policy has the same properties as those of optimal discounted policies investigated by the authors in a previous paper. Finally, we prove that in the absence of costs accrued by messages within the phase, there exists a policy such that the time-average cost tends toward zero as the phase lengthT.     

Presliding friction identification based upon the Maxwell Slip model structure

The problem of presliding friction identification based upon the Maxwell Slip model structure, which is capable of accounting for the presliding hysteresis with nonlocal memory, is considered. The model structure's basic properties are examined, based upon which a priori identifiability is established, the role of initial conditions on identification is investigated, and the necessary and sufficient conditions for a posteriori identifiability are derived. Using them, guidelines for excitation signal design are also formulated. Building upon these results, two new methods, referred to as Dynamic Linear Regression (DLR) and NonLinear Regression (NLR), are postulated for presliding friction identification. Both may be thought of as different extensions of the conventional Linear Regression (LR) method that uses threshold preassignment: The DLR by introducing extra dynamics in the form of a vector finite impulse response filter, and the NLR by relaxing threshold preassignment through a special nonlinear regression procedure. The effectiveness of both methods is assessed via Monte Carlo experiments and identification based upon laboratory signals. The results indicate that both methods achieve significant improvements over the LR. The DLR offers the highest accuracy, with the NLR striking a very good balance between accuracy and parametric complexity.     

A simple load balancing problem with decentralized information

The following load balancing problem is investigated in discrete time: A service system consists of two service stations and two controllers, one in front of each station. The service stations provide the same service with identical service time distributions and identical waiting costs. Customers requiring service arrive at a controller's site and are routed to one of the two stations by the controller. The processes describing the two arrival streams are identical. Each controller has perfect knowledge of the workload in its own station and receives information about the other station's workload with one unit of delay. The controllers' routing strategies that minimize the customers' total flowtime are determined for a certain range of the parameters that describe the arrival process and the service distribution. Specifically, we prove that optimal routing strategies are characterized by thresholds that are either precisely specified or take one of two possible values.     

Optimal batch service of a polling system under partial information

We consider the optimal scheduling of an infinite-capacity batch server in aN-node ring queueing network, where the controller observes only the length of the queue at which the server is located. For a cost criterion that includes linear holding costs, fixed dispatching costs, and linear service rewards, we prove optimality and monotonicity of threshold scheduling policies.     

Informational aspects of a class of subjective games of incomplete information: Static case

Subjective games of incomplete information are formulated where some of the key assumptions of Bayesian games of incomplete information are relaxed. The issues arising because of the new formulation are studied in the context of a class of nonzero-sum, two-person games, where each player has a different model of the game. The static game is investigated in this note. It is shown that the properties of the static subjective game are different from those of the corresponding Bayesian game. Counterintuitive outcomes of the game can occur because of the different beliefs of the players. These outcomes may lead the players to realize the differences in their models.This work was sponsored by the Office of Naval Research under Contract No. N00014-84-C-0485.