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On the transient behavior of the m/m/m/m loss model
Communications in Statistics. Stochastic Models, 1990We develop an asymptotic technique for analyzing the transient behavior of queues and other stochastic models. As an example we consider the Erlang loss model which is the M/M/m/m queue. Asymptotic expansions are constructed for systems with a large number of servers and a large arrival rate that is O(m).
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M Machines, One Repairman (M/M/1/M)
2012This chapter explores a system with a limited number of units in the input population, like M machines in a shop that occasionally require service from one repairman. The inter-arrival time per unit and the service times are exponential. This could be a firm with five copy machines and one repairman. The probability on the number of units in the system
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2012
This chapter considers a series of two systems where the arriving units are treated in one system and then in another system in a tandem way. This could be patients arriving to a medical center where the first system is filling out the paper and insurance forms, and the second system is receiving the medical attention.
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This chapter considers a series of two systems where the arriving units are treated in one system and then in another system in a tandem way. This could be patients arriving to a medical center where the first system is filling out the paper and insurance forms, and the second system is receiving the medical attention.
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M Machines, R Repairmen (M/M/R/M)
2012This chapter pertains for a system with a limited number of units in the input population, like M machines in a shop that occasionally require service from R servers (repairmen). The inter-arrival time per unit and the service times are exponential. An example is a taxi fleet of 100 cabs with four service mechanics on duty to maintain and repair the ...
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2020
A bivariate Markov process {??(t)=(X???(t), X???(t))^T, t???0} whose phase space is a lattice semistrip S(X)={0,1,???, c+m, }xZ??? is considered. The first component X???(t) ???{0,1,..., c +m} indicates the summarized number of busy servers and calls in the queue at the instant t ???0, whereas the second one X???(t)???{0,1,...} is the number of retrial
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A bivariate Markov process {??(t)=(X???(t), X???(t))^T, t???0} whose phase space is a lattice semistrip S(X)={0,1,???, c+m, }xZ??? is considered. The first component X???(t) ???{0,1,..., c +m} indicates the summarized number of busy servers and calls in the queue at the instant t ???0, whereas the second one X???(t)???{0,1,...} is the number of retrial
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