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Industrial & Manufacturing Engineering Publications

Markovian Arrival Process

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Full-Text Articles in Operations Research, Systems Engineering and Industrial Engineering

Queueing-Inventory Models For A Two-Vendor System With Positive Service Times, Srinivas Chakravarthy, Khizer Hayat Jan 2020

Queueing-Inventory Models For A Two-Vendor System With Positive Service Times, Srinivas Chakravarthy, Khizer Hayat

Industrial & Manufacturing Engineering Publications

Queueing-inventory systems wherein the demands are processed with random service times have been getting a lot of attention recently. In such systems, each demand needs one or more inventory items and needs positive processing times. The inventory is generally replenished using -type policy and the lead times are assumed to be random. In this paper we introduce the concept of multiple vendors who will be responsible for the replenishment of inventory. Under the assumptions of a two-vendor system wherein the demands occurring according to a Markovian arrival process, the service times to be of phase type, and the lead times …


A Discrete Single Server Queue With Markovian Arrivals And Phase Type Group Services, Attahiru Sule Alfa, K. Laurie Dolhun, Srinivas R. Chakravarthy Mar 1995

A Discrete Single Server Queue With Markovian Arrivals And Phase Type Group Services, Attahiru Sule Alfa, K. Laurie Dolhun, Srinivas R. Chakravarthy

Industrial & Manufacturing Engineering Publications

We consider a single-server discrete queueing system in which arrivals occur according to a Markovian arrival process. Service is provided in groups of size no more than M customers. The service times are assumed to follow a discrete phase type distribution, whose representation may depend on the group size. Under a probabilistic service rule, which depends on the number of customers waiting in the queue, this system is studied as a Markov process. This type of queueing system is encountered in the operations of an automatic storage retrieval system. The steady-state probability vector is shown to be of (modified) matrix-geometric …


A Finite Capacity Queue With Markovian Arrivals And Two Servers With Group Services, Srinivas Chakravarthy, Attahiru S. Alfa Feb 1994

A Finite Capacity Queue With Markovian Arrivals And Two Servers With Group Services, Srinivas Chakravarthy, Attahiru S. Alfa

Industrial & Manufacturing Engineering Publications

In this paper we consider a finite capacity queuing system in which arrivals are governed by a Markovian arrival process. The system is attended by two exponential servers, who offer services in groups of varying sizes. The service rates may depend on the number of customers in service. Using Markov theory, we study this finite capacity queuing model in detail by obtaining numerically stable expressions for (a) the steady-state queue length densities at arrivals and at arbitrary time points; (b) the Laplace-Stieltjes transform of the stationary waiting time distribution of an admitted customer at points of arrivals. The stationary waiting …