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dc.contributor.authorHAHN, SUSAN ANN
dc.date.accessioned2018-07-12T18:12:19Z
dc.date.available2018-07-12T18:12:19Z
dc.date.issued1982
dc.identifier.citationSource: Dissertation Abstracts International, Volume: 43-04, Section: B, page: 1130.
dc.identifier.urihttp://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:8220404
dc.identifier.urihttps://hdl.handle.net/20.500.12202/2802
dc.description.abstractIn this thesis we consider the system of two unbounded single server queues in which a customer upon arrival joins both queues. The arrivals are assumed to form a Poisson process with mean interarrival time 1 and the servers have exponential service time distribution with means 1/(alpha) and 1/(beta) respectively. It is assumed 1 < (alpha) (LESSTHEQ) (beta) and hence the equilibrium probabilities p(,ij) are positive for all i,j and.;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI).;The functional equation for the generating function.;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI).;is obtained from the equilibrium equations. This equation exhibits a relation between the functions P(z,0), P(0,w) on the algebraic curve S = {lcub}(z,w): (zw)('2) - (1 + (alpha) + (beta))zw + (alpha)w + (beta)z = 0{rcub}. S is parametrized by a pair of elliptic functions z = z(t), w = w(t) and the functional equation is converted into automorphy conditions for A(t) = P(z(t),0) and B(t) = P(0,w(t)), which are then continued analytically to the whole t-plane. A(t) and B(t), and hence P(z,0), P(0,w), P(z,w) are obtained in closed form. Asymptotic formulas for p(,ij) as i,j (--->) (INFIN) are obtained from the expression for P(z,w).
dc.publisherProQuest Dissertations & Theses
dc.subjectMathematics.
dc.titleTWO PARALLEL QUEUES CREATED BY ARRIVALS WITH TWO DEMANDS
dc.typeDissertation


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