NECESSARY AND SUFFICIENT CONDITIONS FOR STABILITY OF A BIN-PACKING SYSTEM

Objects of various integer sizes, o,, o , are to be packed together into bins of size N as they arrive at a service facility. The number of objects of size o, which arrive by time t is A , where the components of A' = (A , * , , A ')' are independent renewal processes, with A'/t - A as t --oo. The empty space in those bins which are neither empty nor full at time t is called the wasted space and the system is declared stabilizable if for some finite B there exists a bin-packing algorithm whose use guarantees the expected wasted space is less than B for all t. We show that the system is stabilizable if the arrival processes are Poisson and A lies in the interior of a certain convex polyhedral cone A. In this case there exists a bin-packing algorithm which stabilizes the system without needing to know A. However, if A lies on the boundary of A the wasted space grows as O(V\t) and if A is exterior to A it grows as O(t); these conclusions hold even if objects may be repacked as often as desired. ONLINE ALGORITHMS; RANDOM WALKS; STOCHASTIC ALGORITHMS