A provably efficient algorithm for dynamic storage allocation
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
First-fit storage of linear lists: tight probabilistic bounds on wasted space
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Data Structure Techniques
Some Asymptotic Results for the M/M/∞ Queue with Ranked Servers
Queueing Systems: Theory and Applications
On the Asymptotic Optimality of First-Fit Storage Allocation
IEEE Transactions on Software Engineering
Storage allocation under processor sharing I: exact solutions and asymptotics
Queueing Systems: Theory and Applications
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We consider models of queue storage, where items arrive accordingly to a Poisson process of rate λ and each item takes up one cell in a linear array of cells, which are numbered {1, 2, 3,...}. The arriving item is placed in the lowest numbered available cell. The total service rate provided to the items is the constant μ (with ρ = λ/μ), but service may be provided simultaneously to more than one item. If there are N items stored and each is serviced at the rate μ/N, this corresponds to processor sharing (PS). We analyze two models of this type, which have been shown to provide bounds on the PS model. We shall assume that (1) the server works only on the left-most item, or (2) on the two rightmost items. The set of occupied cells at any time is {i1, i2,...,iN} where i1 i2 iN and we are interested in the wasted space (iN − N), the maximum occupied cell (iN), and the joint distribution of the wasted space and the number of items in the system (N). We study these exactly and asymptotically, especially in the heavy traffic limit where ρ ↑ 1.