Upper and lower bounds are proved for the shared space requirements for solution of several problems involving resource allocation among asynchronous processes. Controlling the degradation of performance when a limited number of processes fail is of particular interest.

Devices]: Modes of Computation -parallelism General Terms: Algorithms, Performance, Reliability, Theory Additional Key Words and Phrases: Asynchronous system, distributed computing,' FIFO, lower bound, queue, resource allocation, shared memory, space complexity This work was supported in part by the Office of Naval Research under contract N00014-82-K0154; by the U.S. Army Research Office under contract DAAG29-79-C-0155; and by the National Science Foundation under grants MCS77-02474, MCS77-15628, MCS78-01689, MCS-8116678, and DCR-8405478. N. A. Lynch's work was supported by NSF grant CCR-8611442, DARPA N00014-83K -0125, and ONR N00014-85-K-0168.

this paper, the problem is generalized to a distributed system resource allocation problem which is local in two senses. First, although the system and number of users can be very large, there is a limit to the overlap in resource demands of different users. The second condition can be thought of as a property of the geography of the network - the resources are (or can be) located in the network in such a way that connunication between a user and any of its required resources is fast. Both types of locality conditions are satisfied by the Dining Philosophers problem. Under these two conditions, one would hope that waiting chains could be avoided, so that the worst-case time to grant a user's requests is independent of the total size of the network and the total number of users

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