2. First Server Available Queue

considers a queue with common exponential arrival and a finite number ($C$) of distinguishable and ordered servers ($C_i, i = 1..C$). As a client arrives, it will be served by the first available server, i.e., if $C_1$ is available, the client is served by it, otherwise if $C_2$ is available the client is served by it, and so on. This queue behavior is not monotonic, so there is no, at the authors best knowledge, product-form solution for this model. The SAN model describing this queue is presented in Figure. The basic technique to model this queue is to consider each server as an automaton ($A_i$). The arrival in each server is expressed by a local event (called $L_i$) with a functional rate that will be nonzero, e.g., $\lambda$, if all precedent servers are busy, and zero otherwise. At a given moment, only one server, the first available, has a nonzero arrival rate. The end of service at each server is simply a local event ($D_i$) with a constant rate, e.g., $\mu_i$.


The textual .san  files describing this model are:

a.  C= 4                b.  C= 13

Where : 
- C is  the  nomber  of  servers 

Figure :First Server Available Model

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