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Optimal control and performance analysis of an M X / M / 1 queue with batches of negative customers

Jesus R. Artalejo, Antonis Economou (2004)

RAIRO - Operations Research - Recherche Opérationnelle

We consider a Markov decision process for an M X / M / 1 queue that is controlled by batches of negative customers. More specifically, we derive conditions that imply threshold-type optimal policies, under either the total discounted cost criterion or the average cost criterion. The performance analysis of the model when it operates under a given threshold-type policy is also studied. We prove a stability condition and a complete stochastic comparison characterization for models operating under different...

Optimal control and performance analysis of an MX/M/1 queue with batches of negative customers

Jesus R. Artalejo, Antonis Economou (2010)

RAIRO - Operations Research

We consider a Markov decision process for an MX/M/1 queue that is controlled by batches of negative customers. More specifically, we derive conditions that imply threshold-type optimal policies, under either the total discounted cost criterion or the average cost criterion. The performance analysis of the model when it operates under a given threshold-type policy is also studied. We prove a stability condition and a complete stochastic comparison characterization for models operating under different...

Optimal control for a BMAP/SM/1 queue with MAP-input of disasters and two operation modes

Olga V. Semenova (2004)

RAIRO - Operations Research - Recherche Opérationnelle

A single-server queueing system with a batch markovian arrival process (BMAP) and MAP-input of disasters causing all customers to leave the system instantaneously is considered. The system has two operation modes, which depend on the current queue length. The embedded and arbitrary time stationary queue length distribution has been derived and the optimal control threshold strategy has been determined.

Optimal control for a BMAP/SM/1 queue with MAP-input of disasters and two operation modes

Olga V. Semenova (2010)

RAIRO - Operations Research

A single-server queueing system with a batch Markovian arrival process (BMAP) and MAP-input of disasters causing all customers to leave the system instantaneously is considered. The system has two operation modes, which depend on the current queue length. The embedded and arbitrary time stationary queue length distribution has been derived and the optimal control threshold strategy has been determined.

Performance analysis of single server non-markovian retrial queue with working vacation and constant retrial policy

V. Jailaxmi, R. Arumuganathan, M. Senthil Kumar (2014)

RAIRO - Operations Research - Recherche Opérationnelle

This paper analyses an M/G/1 retrial queue with working vacation and constant retrial policy. As soon as the system becomes empty, the server begins a working vacation. The server works with different service rates rather than completely stopping service during a vacation. We construct the mathematical model and derive the steady-state queue distribution of number of customer in the retrial group. The effects of various performance measures are derived.

Product form solution for g-networks with dependent service

Pavel Bocharov, Ciro D'Apice, Evgeny Gavrilov, Alexandre Pechinkin (2004)

RAIRO - Operations Research - Recherche Opérationnelle

We consider a G-network with Poisson flow of positive customers. Each positive customer entering the network is characterized by a set of stochastic parameters: customer route, the length of customer route, customer volume and his service length at each route stage as well. The following node types are considered: (0) an exponential node with c n servers, infinite buffer and FIFO discipline; (1) an infinite-server node; (2) a single-server node with infinite buffer and LIFO PR discipline; (3) a single-server...

Product form solution for g-networks with dependent service

Pavel Bocharov, Ciro D'Apice, Evgeny Gavrilov, Alexandre Pechinkin (2010)

RAIRO - Operations Research

We consider a G-network with Poisson flow of positive customers. Each positive customer entering the network is characterized by a set of stochastic parameters: customer route, the length of customer route, customer volume and his service length at each route stage as well. The following node types are considered: Negative customers arriving at each node also form a Poisson flow. A negative customer entering a node with k customers in service, with probability 1/k chooses one of served positive customer...

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