1,720,978 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
PH/PH/1/r queueing model with the server requiring a search for customers
No full textA single-server queueing system in which the server is required to search for customers in a finite buffer is considered. The
interarrivals times, service times and search times are i.i.d. random variables with probability distribution functions of phasetype.
For the stationary distribution of the underlying Markov process a matrixgeometric solution is obtained
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
Retrial servicing of Poisson flow in a system of finite capacity with customer-searching server
No full textOn a Retrial Single-Server Queuing System with Finite Buffer and Multivariate Poisson Flow
No full textWe consider a single-server queueing system with a finite buffer, Kinput Poisson
ows of intensities λi, and distribution functions Bi(x) of service times for calls of the i-th type,
i= 1...K. If the buffer is overflowed, an arriving call is sent to the orbit and becomes a repeat
call. In a random time, which has exponential distribution, the call makes an attempt to reenter
the buffer or server, if the latter is free. The maximum number of calls in the orbit is limited;
if the orbit is overflowed, an arriving call is lost. We find the relation between steady-state
distributions of this system and a system with one Poisson flow of intensity λ=∑_{i=1}^{K}λi
where type i of a call is chosen with probability λi/λ at the beginning of its service. A numerical
example is given
On a Retrial Single-Server Queueing System with Finite Buffer and Poisson Flow
No full textA retrial single-server queueing system with finite buffer is considered. The primary incoming flow is Poissonian. If the buffer is overflown, a call entering the system becomes a repeat call and joins the group of repeat calls referred to as an orbit. The maximum number of calls that can simultaneously be contained in the orbit is limited. A call from the orbit makes new attempts to enter the system until a vacancy occurs. Time between repeat attempts for each call is an exponentially distributed random variable. At the initial moment of service, a type of a call is defined: with probability ai it becomes a call of type i and its service time in this case has distribution function Bi(x), i = 1,K. For this system, the stationary joint distribution of queues in the buffer and orbit is found. Numerical examples are given
Retrial servicing of multivariate Poisson flow with customer-searching server with finite buffer
No full textThe MAP/MSP/1/r Queueing System With Background Customers
No full textA single server queueing system with Markov flow of principal customers and background
customers arriving from infinite reserve source is studied. The Markov service processes of customers
of both types are considered. The system has a finite buffer for principal customers. The
service discipline is characterized by non-preemptive priority of principal customers respect to
background customers. An effective matrix-recurrent algorithm for the calculation of the stationary
state probabilities of the underlying Markov process is derived
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
- …
