  WiFi offloading, where mobile device users (e.g., smart phone users) transmit
packets through WiFi networks rather than cellular networks, is a promising
solution to alleviating the heavy traffic burden of cellular networks due to
data explosion. However, since WiFi networks are intermittently available, a
mobile device user in WiFi offloading usually needs to wait for WiFi connection
and thus experiences longer delay of packet transmission. To motivate users to
participate in WiFi offloading, cellular network operators give incentives
(rewards like coupons, e-coins) to users who wait for WiFi connection and
transmit packets through WiFi networks.
  In this paper, we aim at maximizing users' rewards while meeting constraints
on queue stability and energy consumption. However, we face scheduling
challenges from random packet arrivals, intermittent WiFi connection and time
varying wireless link states. To address these challenges, we first formulate
the problem as a stochastic optimization problem. We then propose an optimal
scheduling policy, named Optimal scheduling Policy under Energy Constraint
(OPEC), which makes online decisions as to when to delay packet transmission to
wait for WiFi connection and which wireless link (WiFi link or cellular link)
to transmit packets on. OPEC automatically adapts to random packet arrivals and
time varying wireless link states, not requiring a priori knowledge of packet
arrival and wireless link probabilities. As verified by simulations, OPEC
scheduling policy can achieve the maximum rewards while keeping queue stable
and meeting energy consumption constraint.
