I will first discuss the general problem of determining asymptotics of the coefficients of a multivariate generating function. Next, I will discuss the special case where the function is the product of reciprocals of linear terms, arising for example in queuing applications (see [BM93]). It is possible in this case to give a precise algorithm for computing a finite collection of asymptotic formulae. I will present this, with indications of proofs. If time permits, I will discuss to what degree we know how to find such an algorithm in more general cases.
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