An approximation algorithm for the generalized assignment problem
Mathematical Programming: Series A and B
Self-buffering, self-balancing, self-flushing production lines
Management Science
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximation Algorithms for Single-Source Unsplittable Flow
SIAM Journal on Computing
On the k-Splittable Flow Problem
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Dynamic Server Allocation for Queueing Networks with Flexible Servers
Operations Research
Maximum Pressure Policies in Stochastic Processing Networks
Operations Research
Throughput Maximization for Tandem Lines with Two Stations and Flexible Servers
Operations Research
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We study a queueing network where customers go through several stages of processing, with the class of a customer used to indicate the stage of processing. The customers are serviced by a set of flexible servers, i.e., a server may be capable of serving more than one class of customer and the sets of classes that the servers are capable of serving may overlap. We would like to choose an assignment of servers that achieves the maximal capacity of the given queueing network, where the maximal capacity is λ* if the network can be stabilized for all arrival rates λ λ* and cannot possibly be stabilized for all λ λ*. We examine the situation where there is a restriction on the number of servers that are able to serve a class, and reduce the maximal capacity objective to a maximum throughput allocation problem of independent interest: the Total Discrete Capacity Constrained Problem(TDCCP). We prove that solving TDCCP is in general NP-complete, but we also give exact or approximation algorithms for several important special cases.