is this a queueing system?

From: Yan ZHANG (buaanupt_at_sina.com)
Date: 11/02/04 

Date: Tue, 2 Nov 2004 11:51:35 +0800

In a system,
1. the arrival process is Poisson process with arrival rate lambda.
2. there are C maximumal servers.
3. Let t_n (n=1,2...) be the instant of customer arrival.
       (1) At t_1, the first customer arrives, it will consume one server
and this server is deleted. C-1 server are left unused.
       (2) At t_2, the second customer arrives, it will consume one server
and this server is deleted. C-2 server are left unused. This process
continues. At t_C, the C-th customer arrives, it will consume the last
server. No server are available at this instant.
       (3) At t_{C+1}, the (C+1)-th customer arrives, it finds that ther is
no server available, then C servers are added to the system and the system
has C servers again. Now, the (C+1)-th customer can consume one server and
this server is deleted.
       (4) The similar behavor will continue.

I hope to know the probability that there is no server available upon the
moment of an customer arrival. It seems to me that the probabilty is
1/(C+1). Is this understanding correct? or what type of this queueing
system? Can you plz give some suggestions for this or reference or key words
or link?

Thank you very much for your attention and any comments. 

-- 
Yan ZHANG
http://www.ntu.edu.sg/home5/pg01308021

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