Two online algorithms for the ambulance systems

Abstract

An ambulance system consists of a collectionS={s ₁,...s_m} of emergency centers in a metric spaceM. Each emergency centers _i has a positive integral capacityc _i to denote, for example, the number of ambulances at the center. There aren = Σ ^m _{i = 1} c _i patients requiring ambulances at different timest _j and every patient is associated with a numberb _j, the longest time during which the patient can wait for ambulance. An online algorithmA will decide which emergency center sends an ambulance to serve a request for ambulance from a patient at some time. If algorithmA sends an ambulance ins _i to serve a patientr _j, then it must be observed thatd _i,j/v<b_j, whered _i,j is the distance between emergency centers _i and patientr _j, andv is the velocity of ambulance. A fault of algorithmA is such that to a request for ambulance at some timet _j withj≤n, for everyi withd _i,j/v<b_j, there is no ambulance available ins _i. The cost of an algorithmA is the number of faultsA makes. This paper gives two algorithmsB andC, whereB is the local greedy algorithm andC is a variant of balancing costs, and proves that bothB andC have no bounded competitive ratios. Moreover, given any sequence σ of requests for ambulances without optimal faults, the cost ofC on σ is less than or equal to [n/3] and that ofB is less than or equal to [n/2].