Adaptive Bin Packing with Overflow

Motivated by bursty bandwidth allocation and the of virtual machines to servers in cloud, we consider online problem packing items with random sizes into unit-capacity bins. Items arrive sequentially, but on arrival, an item’s actual size is unknown; only its probabilistic information available decision maker. Without knowing this size, maker must irrevocably pack item bin or place it a new bin. Once packed bin, observes overflowing possibility. An overflow incurs large penalty cost, corresponding unusable for rest process. In practical terms, models delayed services, failure servers, and/or loss end-user goodwill. The objective minimize total expected cost given sum number opened bins cost. We present algorithm at most constant factor times incurred optimal policy when are drawn from independent identically distributed (i.i.d.) sequence unknown length. give similar result distributions exponential arbitrary rates. also study offline model, where known advance be sequentially. construct soft-capacity polynomial-time approximation scheme show that complexity computing [Formula: see text]-hard. Finally, provide empirical our algorithm’s performance.