Ambiguity resolution "on-the-fly" procedures are designed to deliver in real time the integer biases that give full access to the accurate pseudorange information contained within the GPS carrier phase measurements. The key performance parameters of these procedures are their time of convergence and error rate, usually estimated from experience but rarely analytically determined. Using results derived for a multiple hypotheses sequential test called the M-ary Sequential Probability Ratio Test (MSPRT), this paper presents a theoretical analysis of the performance parameters of the Maximum A Posteriori Ambiguity Search (MAPAS) procedure. In particular, expressions of bounds and asymptotic values of the expected stopping time and error probability of MAPAS are determined as functions of the decision threshold, thus providing a means to control the performances. This study shows the influence of the number of satellites as well as the importance of the mode of selection of the primary satellites. The figures obtained are checked against observed values, showing the validity of the determined bounds and the consistency of the asymptotic values, although they lack accuracy when the number of satellites is low.