A multiserver queue with narrow- and wide-band customers and wide-band restricted access

TitleA multiserver queue with narrow- and wide-band customers and wide-band restricted access
Publication TypeJournal Article
Year of Publication1988
AuthorsDe Serres, Y., and L. G. Mason
JournalCommunications, IEEE Transactions on
Start Page675
Pagination675 -684
Date PublishedJun/1988
Keywordsblocked customers, blocking, broadband networks, cutoff parameter, delay, matrix-geometric techniques, mean waiting time, moment-generating functions, multiserver queue, narrow-band customers, queueing theory, restricted access, service facility, single server, system performance, wide-band customers, wide-band restricted access

We consider a multiserver queueing system with two classes of customers: a type 1 (narrow-band, NB) customer requires a single server, while each type 2 (wide-band, WB) customer requests n of the m servers (n is not random). Servers allocated to a type 2 customer are seized and released simultaneously. Service times are exponentially distributed with mean l/p, for type i customers (i = 1,2). Blocked type 1 customers are cleared while blocked type 2 customers may be delayed in an infinite
waiting room. A type 1 customer enters service immediately upon arrival if at least one server is free, irrespective of the status of the type 2 queue. WB customers have restricted access to the service facility; a cutoff parameter specifies the maximum number of type 2 customers that can be in service at the same time. Two approaches, moment-generating functions and matrix-geometric techniques, are considered for the computation of the system performance; that is, the mean waiting time in queue and the probability of delay (i.e., nonzero waiting time) for type 2 customers, as well as the probability of blocking for type 1 customers.

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