Dynamic Bandwidth Allocation for Low Power Devices With Random Connectivity

In this paper we consider the bandwidth allocation problem where multiple low power wireless devices share a common time-slotted channel for transmitting to a single server. Due to energy constraints, these devices alternate between common active and inactive periods, the former typically much smaller than the latter. At the beginning of each active period the server decides which user(s) can access the common channel. This decision is based on the knowledge of the current backlog and connectivity of each queue. In each time slot an active user may or may not be connected to the server. If a user is connected to the server, it can transmit with a certain success probability. Arrivals are arbitrary and there is a cost for holding a packet in the queue. Different queues have different packet holding costs leading to differentiated services. We consider the problem of minimizing the total discounted cost over a finite or infinite horizon and provide sufficient conditions under which a greedy policy is optimal. We consider two connectivity models: (1) there is no information about connectivity statistics, and (2) connectivity probability is independent from one time slot to the other (memoryless channel). We show that in each of these cases it is optimal to serve the user with the highest one step reward (smallest one step cost) if this gain is sufficiently larger than that from serving the other users. The sufficient condition is shown to be asymptotically tight in special cases. We then use numerical examples to study the performance of the greedy policy as a function of the duty cycle and the length of the active period. This helps us to better understand and model the tradeoff between increasing the lifetime and decreasing the packet delay in such systems