In vehicular cloud computing (VCC) systems, the computational resources ofmoving vehicles are exploited and managed by infrastructures, e.g., roadsideunits, to provide computational services. The offloading of computational tasksand collection of results rely on successful transmissions between vehicles andinfrastructures during encounters. In this paper, we investigate how to providetimely computational services in VCC systems. In particular, we seek tominimize the deadline violation probability given a set of tasks to be executedin vehicular clouds. Due to the uncertainty of vehicle movements, the taskreplication methodology is leveraged which allows one task to be executed byseveral vehicles, and thus trading computational resources for delay reduction.The optimal task replication policy is of key interest. We first formulate theproblem as a finite-horizon sampled-time Markov decision problem and obtain theoptimal policy by value iterations. To conquer the complexity issue, we proposethe balanced-task-assignment (BETA) policy which is proved optimal and has aclear structure: it always assigns the task with the minimum number ofreplicas. Moreover, a tight closed-form performance upper bound for the BETApolicy is derived, which indicates that the deadline violation probabilityfollows the Rayleigh distribution approximately. Applying the vehiclespeed-density relationship in the traffic flow theory, we find that vehiclemobility benefits VCC systems more compared with road traffic systems, byshowing that the optimum vehicle speed to minimize the deadline violationprobability is larger than the critical vehicle speed in traffic theory whichmaximizes traffic flow efficiency.
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