We study a parallel service queueing system with servers of types s_1,\ldots,s_J, customers of types c_1,\ldots,c_I, bipartite compatibility graph \mathcal{G . For a general renewal stream of arriving customers and general service time distributions, the behavior of such systems is very complicated , in particular the calculation of matching rates r_{c_i,s_j , the fraction of services of customers of typec_i by servers of type s_j , is intractable. We suggest through a heuristic argument that if the number of servers becomes large, the matching rates are well approximated by matching rates calculated from the tractable FCFS bipartite infinite matching model. We present simulation evidence to support this heuristic argument, and show how this can be used to design systems for given performance requirements.
We study a parallel queueing system with multiple types of servers and customers. A bipartite graph describes which pairs of customer-server types are compatible. We consider the service policy that always assigns servers to the first, longest waiting compatible customer, and that always assigns customers to the longest idle compatible server if on arrival, multiple compatible servers are available . For a general renewal stream of arriving customers and general service time distributions, the behavior of such systems is very complicated . In particular, the calculation of matching rates , the fraction of services of customer-server type , is intractable. We suggest through a heuristic argument that if the number of servers becomes large, the matching rates are well approximated by matching rates calculated from the tractable bipartite infinite matching model. We present simulation evidence to support this heuristic argument, and show how this can be used to design systems with desired performance requirements.
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service
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servers of types s_1,\ldots,s_J, customers of types c_1,\ldots,c_I, bipartite compatibility graph \mathcal{G
multiple types of servers and customers. A bipartite graph describes which pairs of customer-server types are compatible. We consider the service policy that always assigns servers to the first, longest waiting compatible customer, and that always assigns customers to the longest idle compatible server if on arrival, multiple compatible servers are available
R
, in particular
. In particular,
D
r_{c_i,s_j
R
customers of typec_i by servers of type s_j
customer-server type
D
FCFS
R
for given
with desired