102,238 research outputs found
Product Form Solution for a G-Network with Signals And Impatient Service
No full textThis paper presents some results on an exponential queuing network with signals and impatient service. Positive customers and signals arrive to each node according to a Poisson process. When the service is finished in a node, a positive customer moves to another node with fixed probabilities either as a positive customer or as a signal, or quits the network. Every signal is activated during a random exponentially distributed amount of time. Activated signals with fixed probabilities either move a customer from the node they arrive to another node or kill a positive a customer. Each customer can be served in a node at most a random time (“patient” time) distributed exponentially. When the patient service is finished, the customer with fixed probabilities state probabilities od such G-network in the case of positive customers processed by a single server in each node as well as in the case of an analogous symmetrical G-network in which service rate of a positive customer in a node depends on its state
Impatient service in a G-network
No full textAn open exponential queueing network with signals and impatient service is considered.
Upon completion of service at a node, a positive customer passes to another node with fixed probabilities either as a positive customer or as a signal, or quits the network. Every signal is activated during a random exponentially distributed
amount of time. Activated signals with fixed probabilities either move a customer from the node they arrive to another node or kill a positive customer. Each customer can be served in a node at most a random time (”patient” time) distributed exponentially.
When the patient service is finished, the customer with fixed robabilities either goes to another node or quits the network. The stationary state probabilities for such a G-network in which positive customers are processed in each node by a single server is derived in product form. The solution for an analogous symmetrical G-network in which service rate of a positive customer at each node depends on the number of positive customers in this node is expressed in product form too
Product form solution for g-networks with dependent service
No full textWe 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. 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 node with infinite buffer and PS discipline. Negative customers arriving at each node also form a Poisson flow. A negative customer entering a node with k customers in service, with probability Ilk chooses one of served positive customer as a "target". Then, if the node is of a type 0 the negative customer immediately "kills" (displaces from the network) the target customer, and if the node is of types 1-3 the negative customer with given probability depending on parameters of the target customer route kills this customer and with complementary probability he quits the network with no service. A product form for the stationary probabilities of underlying Markov process is obtained
Retrial servicing of Poisson flow in a system of finite capacity with customer-searching server
No full textRetrial servicing of multivariate Poisson flow with customer-searching server with finite buffer
No full textMultiplicative solution for exponential G-networks with dependent service and preemptive resume of service of killed customers
No full textG-networks with Poisson flow of positive customers,
multi-server exponential nodes, and dependent service
at the different nodes are studied. Every customer
arriving at the network is defined by a set
of random parameters: customer route, the length
of customer route, customer volume and his service
time at each route stage as well. A killed positive
customer is removed at the last place in the queue
and quits the network just after his remaining service
time will be elaborated. Product form solution
for multidimensional stationary distribution of the
network state is derived
Product form solution for exponential G-networks with dependent service and completion of service of killed customers
No full textDynamic routing, Communication networks, Mutiobjective Optimisation, Heuristics,
The Stationary Characteristics of the G/MSP/1/r queueing system
No full textA single-server queueing system with recurrent input
ow and Markov service process
is considered. Both the cases of finite and infinite buffers are investigated. The analysis of this
system is based on the method of embedded Markov chain. The main stationary characteristics
of system performance are derived
A retrial queueing system with a finite buffer, several input flows and a customer-searching server
No full textWe consider a single-server retrial queueing system with K Poisson flows of customers, which arrive to a buffer of finite capacity. If a customer upon arrival finds the buffer full, he joins an orbit of limited capacity in order to return to the queue again after an exponentially distributed time interval. An arriving customer is lost if he finds the buffer and orbit fully occupied. The service time of an i-type customer has an arbitrary distribution function Bi(x). Every service completion is followed by a search phase with exponentially distributed duration to seek for the next customer for service. Customers are taken by the server from the queue according to the FCFS discipline.
It is proved that the analysis of this queueing system is reduced to the analysis of a similar queueing system but with only one Poisson flow
The M/G/1/r Queueing System with Finite Buffer and Retrials
No full textA single-server retrial queueing system with finite buffer, Poisson arrivals and arbitrary distribution of service time is considered. If a customer from outside finds the buffer completely occupied he joins a finite retrial queue (or orbit) in order to seek service again after an exponentially distributed interval of time. In case an arriving customer finds the buffer and the retrial queue completely full he is lost. The stationary distribution of underlying Markov process is derived
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