scholarly journals On the asymptotic behaviour of M/G/1 retrial queues with batch arrivals and impatience phenomenon

2012 ◽  
Vol 55 (3-4) ◽  
pp. 654-665 ◽  
Author(s):  
Nawel K. Arrar ◽  
Natalia V. Djellab ◽  
Jean-Bernard Baillon
Keyword(s):  
Asymptotic Behaviour ◽  
Retrial Queues ◽  
Batch Arrivals

scholarly journals Stability of retrial queues with versatile retrial policy

2006 ◽  
Vol 2006 ◽  
pp. 1-16 ◽  
Author(s):  
Tewfik Kernane ◽  
Amar Aïssani
Keyword(s):  
Poisson Process ◽  
Strong Coupling ◽  
Sufficient Conditions ◽  
Retrial Queues ◽  
Negative Customers ◽  
Batch Arrivals ◽  
Unreliable Server ◽  
Service Times ◽  
The Stability

We consider in this paper the stability of retrial queues with a versatile retrial policy. We obtain sufficient conditions for the stability by the strong coupling convergence to a stationary ergodic regime for various models of retrial queues including a model with two types of customers, a model with breakdowns of the server, a model with negative customers, and a model with batch arrivals. For all the models considered we assume that the service times are general stationary ergodic and interarrival and retrial times are i.i.d. sequences exponentially distributed. For the model with unreliable server we also assume that the repair times are stationary and ergodic and the occurrences of breakdowns follow a Poisson process.

Asymptotic behaviour of sample weighted circuits representing recurrent Markov chains

1990 ◽  
Vol 27 (03) ◽  
pp. 545-556 ◽  
Author(s):  
S. Kalpazidou
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Asymptotic Behaviour ◽  
Probabilistic Interpretation ◽  
Stationary Markov Chain

The asymptotic behaviour of the sequence (𝒞 n (ω), wc,n (ω)/n), is studied where 𝒞 n (ω) is the class of all cycles c occurring along the trajectory ωof a recurrent strictly stationary Markov chain (ξ n ) until time n and wc,n (ω) is the number of occurrences of the cycle c until time n. The previous sequence of sample weighted classes converges almost surely to a class of directed weighted cycles (𝒞∞, ω c ) which represents uniquely the chain (ξ n ) as a circuit chain, and ω c is given a probabilistic interpretation.

scholarly journals Recent Results in Finite‐source Retrial Queues with Collisions

2021 ◽  
pp. 213-258
Author(s):  
Anatoly Nazarov ◽  
János Sztrik ◽  
Anna Kvach
Keyword(s):  
Retrial Queues ◽  
Finite Source

Entropy numbers of embedding maps between Besov spaces with an application to eigenvalue problems

1981 ◽  
Vol 90 (1-2) ◽  
pp. 63-70 ◽  
Author(s):  
Bernd Carl
Keyword(s):  
Banach Space ◽  
Asymptotic Behaviour ◽  
Besov Spaces ◽  
Eigenvalue Problems ◽  
Function Spaces ◽  
Sequence Spaces ◽  
Entropy Numbers ◽  
Diagonal Operators

SynopsisIn this paper we determine the asymptotic behaviour of entropy numbers of embedding maps between Besov sequence spaces and Besov function spaces. The results extend those of M. Š. Birman, M. Z. Solomjak and H. Triebel originally formulated in the language of ε-entropy. It turns out that the characterization of embedding maps between Besov spaces by entropy numbers can be reduced to the characterization of certain diagonal operators by their entropy numbers.Finally, the entropy numbers are applied to the study of eigenvalues of operators acting on a Banach space which admit a factorization through embedding maps between Besov spaces.The statements of this paper are obtained by results recently proved elsewhere by the author.

Sign in / Sign up

Export Citation Format

Share Document