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Cari colleghi,<br>
<br>
vi segnalo il prossimo seminario di ED a Tor Vergata, ricordandovi
la pagina web del seminario stesso all' indirizzo
<a class="moz-txt-link-freetext" href="http://www.mat.uniroma2.it/~castorin/Seminario-PDE.html">http://www.mat.uniroma2.it/~castorin/Seminario-PDE.html</a> :<br>
<br>
<h2>Martedi' 21 Gennaio 2014, h 14:15, Aula Dal Passo </h2>
<h2>Carlo Lancia (Universita' di Roma "Tor Vergata")
</h2>
<h2>"Power series approximation of the EDA/D/1 system"<br>
<br>
Consider the arrival process defined by $t_i = i + \xi_i$, where
$\xi_i$ are i.i.d random variables. First introduced in the 50's,
this point process is of remarkable importance in transportation
systems, where scheduled arrivals are intrinsically subject to
random variations; the model has also proved capable of delivering
a good description of actual job arrivals in health care and crane
handling systems.
In this talk I will consider a queueing model where the customers
arrival time are defined as above, and the service is delivered by
a unique server at deterministic times.
Such a queueing model shows an excellent fit with actual data from
the London Heathrow International Airport.
In the case where the delays $\xi_i$ are exponentially
distributed, the queueing model above is represented by the code
EDA/D/1 in the Kendall's notation. I will describe the EDA/D/1
model as a bivariate Markov chain and obtain a functional equation
for the bivariate generating function of the chain stationary
distribution.
Solving that functional equation for the bivariate generating
function is a very tough problem. A possible strategy to solve
this problem is to consider a power series approximation in a
parameter related to the standard deviation of the delays. I will
first show the solution arising from the power series
approximation, and then discuss its pros and cons.
</h2>
<br>
<pre class="moz-signature" cols="72">--
Daniele Castorina
Dipartimento di Matematica - Studio 1221
Università di Roma "Tor Vergata"
Via della Ricerca Scientifica 00133 Roma
email: <a class="moz-txt-link-abbreviated" href="mailto:castorin@mat.uniroma2.it">castorin@mat.uniroma2.it</a>
tel: +390672594653</pre>
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