Performance models must solve quickly even for large systems, to be useful in searching for changes that might give improvements. Thus, efficient solution is important, and is stressed in the Layered Queueing Network Solver (LQNS). This thesis introduces two approximations that approximate the queue states by binomial probabilities, to estimate the waiting time for multiservers (such as multi-threaded tasks or multi-core CPUs). Accuracy and speed of convergence were evaluated for one and for multiple classes of customers. The binomial approximations are compared with the "Rolia-Franks" approximation which is a relatively fast approximation that is currently used in the LQNS model-solving tool. One of the approximations (called the "Arrival-Theorem Binomial", or AB) is better, with smaller error in most cases. A novel approach for dealing with multiple classes is also evaluated, and a case study is included in which the AB approximation is combined with an LQNS solution.