Abstract
In this paper, the minimum-length scheduling problem in wireless networks is studied, where each source of traffic has a finite amount of data to deliver to its corresponding destination. Our objective is to obtain a joint scheduling and rate control policy to minimize the total time required to deliver this finite amount of data from all sources. First, networks with time-invariant channels are considered. An optimal solution is provided by formulating the minimum-length scheduling problem as finding a shortest path on a single-source directed acyclic graph. However, finding the shortest paths is computationally hard since the number of vertices and edges of the graph increases exponentially in the number of network nodes, as well as in the initial traffic demand values. Toward this end, a simplified version of the problem is considered for which we explicitly characterize the optimal solution. Next, our results are generalized to time-varying channels. First, it is shown that in case of time-varying channels, the minimum-length scheduling problem can be formulated as a stochastic shortest path problem and then an optimal policy is provided that is based on stochastic control. Finally, our analytical results are illustrated with a set of numerical examples.
Highlights
The problem of minimum-length scheduling involves obtaining a sequence of activations of wireless nodes so that a finite amount of data residing at a subset of the nodes in the network reaches its intended destinations in minimum time
We provide an explicit characterization of an optimal policy for a simplified, continuous-time model that is obtained by reducing the set of feasible scheduling and rate control decisions to either transmission in the “one at a time” fashion, as in Time Division Multiple Access (TDMA), or in the “all together” mode
We provide an optimal graph-theoretic algorithm by mapping it to a shortest path problem on a directed acyclic graph (DAG), and in the sequel, we give an explicit characterization of the optimal policy for a reduced version of this problem
Summary
The problem of minimum-length scheduling involves obtaining a sequence of activations of wireless nodes so that a finite amount of data residing at a subset of the nodes in the network reaches its intended destinations in minimum time. In [5], the authors consider the problem of obtaining a schedule of minimum length under the SINR interference model They assume that the transmission rates are fixed and that each transmitting node selects optimally its transmission power. We first assume a slotted-time model and formulate the minimum-length scheduling problem as a shortest path between a given source-destination pair on a DAG. We provide an explicit characterization of an optimal policy for a simplified, continuous-time model that is obtained by reducing the set of feasible scheduling and rate control decisions to either transmission in the “one at a time” fashion, as in TDMA, or in the “all together” mode. We are interested in obtaining optimal policies that take joint scheduling and rate control decisions under the objective of minimizing the (expected) time to deliver all data to the intended destinations. We proceed to formulate the minimum-length scheduling problem for static and time-varying networks
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