Delay-energy tradeoff in multicast scheduling for green cellular systems

Multicast transmission based on real-time network state information is a resource-friendly technique to improve the energy efficiency and reduce the traffic burden for cellular systems. This paper evaluates the effectiveness of this technique for downlink transmissions. In particular, a scenario is considered in which multiple mobile users (MUs) asynchronously request to download one common message locally cached at a base station (BS). Due to the randomness of both the channel conditions and the request arrivals from the MUs, the BS may choose to intelligently hold the arrived requests, especially when the channel conditions are bad or the number of requests is small, and then serve them in one shot later via multicasting. Clearly it is of great interest to balance the delay (incurred by holding the requests) and the energy efficiency (EE, defined as the energy cost per request), and this motivates us to quantify the fundamental tradeoff for the proposed 'hold-then-serve' scheme. For the scenario with single channel and unit message sizes, it is shown that for a fixed channel bandwidth, the delay-EE tradeoff reduces to judiciously choosing the optimal stopping rule for when to serve all the arrived requests, where the effect of the bandwidth on the achievable delay-EE region is discussed further. By using optimal stopping theory, it is shown that the optimal stopping rule exists for general Markov channel models and request arrival processes. Particularly, for the hard deadline and proportional delay penalty cases, it is shown that the optimal stopping rule exhibits a threshold structure, and the corresponding threshold in the former case is time varying while in the latter case it is a constant. Finally, for the more general scenario with multiple channels and arbitrary message sizes, the optimal scheduling is formulated as a Markov decision process problem, where some efficient suboptimal scheduling algorithms are proposed.