This paper concerns an approximate analysis of a Markovian multiserver infinite source retrial queuing with impatience, in which all the servers are subject to breakdown and repairs. Customer who find the total number of busy and failed servers equal to s,i.e, he is given to choice to enter a retrial orbit for an random amount of time before attempting to reccess an available server or enter the queue of size q. Customer waiting in the queue start being served as an idle or repaired server assigned to them, they can also leave the queue and enter orbit due to impatience. Customers whose service is interrupted by a failure may have the option of leaving the system entirely or returning to the orbit to repeat or resume service. We assume that each server has its own dedicated repair person, and repairs begin immediately following a failure and all process are assumed to be mutually independent. The simultaneous effect of customer balking, impatience and retrials is analyzed. We try to approximate the steady-state joint distribution of the number of customers in orbit and the number of customers in the service area using a phase-merging Algorithm.
We introduce a non-parametric estimation of the trimmed regression by using
the local linear method of a censored scalar response variable, given a
functional covariate. The main result of this work is the establishment of
almost complete convergence for the constructed estimator. A simulation
study is carried out to compare the finite sample performance based on the
mean square error between the classic local linear regression estimator and
the trimmed local linear regression estimator. Moreover, a real data study
is used to illustrate our methodology.
We investigate an optimal consumption and investment problem for Black-Scholes type financial market on the whole investment interval [0, T ]. We formulate various utility maximization problem, which can be solved explicitly. The method of solution uses the convex dual function (Legendre transform) of the utility function. Related to this concept, we introduce and study the convex dual of the value function for our problem.
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