Dynamic Bin Packing for On-Demand Cloud Resource Allocation.

Dynamic Bin Packing (DBP) is a variant of classical bin packing, which assumes that items may arrive and depart at arbitrary times. Existing works on DBP generally aim to minimize the maximum number of bins ever used in the packing. In this paper, we consider a new version of the DBP problem, namely, the MinTotal DBP problem which targets at minimizing the total cost of the bins used over time. It is motivated by the request dispatching problem arising from cloud gaming systems. We analyze the competitive ratios of the modified versions of the commonly used First Fit, Best Fit, and Any Fit packing (the family of packing algorithms that open a new bin only when no currently open bin can accommodate the item to be packed) algorithms for the MinTotal DBP problem. We show that the competitive ratio of Any Fit packing cannot be better than \mu +1<alternatives> <inline-graphic xlink:type="simple" xlink:href="li-ieq1-2393868.gif"/></alternatives>, where \mu<alternatives><inline-graphic xlink:type="simple" xlink:href="li-ieq2-2393868.gif"/></alternatives> is the ratio of the maximum item duration to the minimum item duration. The competitive ratio of Best Fit packing is not bounded for any given \mu<alternatives> <inline-graphic xlink:type="simple" xlink:href="li-ieq3-2393868.gif"/></alternatives>. For First Fit packing, if all the item sizes are smaller than <alternatives> <inline-graphic xlink:type="simple" xlink:href="li-ieq4-2393868.gif"/></alternatives> of the bin capacity ( \beta >1<alternatives><inline-graphic xlink:type="simple" xlink:href="li-ieq5-2393868.gif"/></alternatives> is a constant), the competitive ratio has an upper bound of \frac\beta \beta -1\cdot \mu + \frac3\beta \beta -1+1<alternatives> <inline-graphic xlink:type="simple" xlink:href="li-ieq6-2393868.gif"/></alternatives>. For the general case, the competitive ratio of First Fit packing has an upper bound of 2\mu + 7 <alternatives><inline-graphic xlink:type="simple" xlink:href="li-ieq7-2393868.gif"/></alternatives>. We also propose a Hybrid First Fit packing algorithm that can achieve a competitive ratio no larger than \frac54\mu + \frac194<alternatives><inline-graphic xlink:type="simple" xlink:href="li-ieq8-2393868.gif"/> </alternatives> when $\mu$<alternatives> <inline-graphic xlink:type="simple" xlink:href="li-ieq9-2393868.gif"/></alternatives> is not known and can achieve a competitive ratio no larger than $\mu + 5$<alternatives> <inline-graphic xlink:type="simple" xlink:href="li-ieq10-2393868.gif"/></alternatives> when $\mu$<alternatives><inline-graphic xlink:type="simple" xlink:href="li-ieq11-2393868.gif"/></alternatives> is known. [ABSTRACT FROM AUTHOR]