Vessels Arrival Process and its Application to the SHIP/M/$$\infty$$ Queue
In modeling of port dynamics it seems reasonable to assume that the ships arrive on a somewhat scheduled basis and that there is a constant lay period during which, in a uniform way, each vessel can arrive at the port. In the present paper, we study the counting process N ( t ) which represents the...
Uloženo v:
| Vydáno v: | Methodology and computing in applied probability Ročník 25; číslo 1 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
01.03.2023
|
| ISSN: | 1387-5841, 1573-7713 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Shrnutí: | In modeling of port dynamics it seems reasonable to assume that the ships arrive on a somewhat scheduled basis and that there is a constant lay period during which, in a uniform way, each vessel can arrive at the port. In the present paper, we study the counting process
N
(
t
) which represents the number of scheduled vessels arriving during the time interval (0,
t
],
$$t>0$$
t
>
0
. Specifically, we provide the explicit expressions of the probability generating function, the probability distribution and the expected value of
N
(
t
). In some cases of interest, we also obtain the probability law of the stationary counting process representing the number of arrivals in a time interval of length
t
when the initial time is an arbitrarily chosen instant. This leads to various results concerning the autocorrelations of the random variables
$$X_i$$
X
i
,
$$i\in \mathbb {Z}$$
i
∈
Z
, which give the actual interarrival time between the
$$(i-1)$$
(
i
-
1
)
-th and the
i
-th vessel arrival. Finally, we provide an application to a stochastic model for the queueing behavior at the port, given by a queueing system characterized by stationary interarrival times
$$X_i$$
X
i
, exponential service times and an infinite number of servers. In this case, some results on the average number of customers and on the probability of an empty queue are disclosed. |
|---|---|
| ISSN: | 1387-5841 1573-7713 |
| DOI: | 10.1007/s11009-023-10003-8 |