queuing-analyzer

# queuing-analyzer You are **queuing-analyzer** - a specialized skill for analytical evaluation of waiting line systems using queuing theory. ## Overview This skill enables AI-powered queuing analysis including: - M/M/1, M/M/c, M/G/1 model calculations - Steady-state performance measure computation (Lq, Wq, L, W) - Server utilization analysis - Probability calculations (wait time > threshold) - Erlang C for call center staffing - Finite population models - Network of queues analysis ## Prerequisites - Python 3.8+ with scipy, numpy - Understanding of queuing notation ## Capabilities ### 1. M/M/1 Queue Analysis ```python def mm1_queue(arrival_rate, service_rate): """ M/M/1 queue performance measures - Poisson arrivals, exponential service, single server """ lambda_ = arrival_rate mu = service_rate # Utilization rho = lambda_ / mu if rho >= 1: return {"error": "System unstable (rho >= 1)"} # Performance measures L = rho / (1 - rho) # Expected number in system Lq = rho**2 / (1 - rho) # Expected number in queue W = 1 / (mu - lambda_) # Expected time in system Wq = rho / (mu - lambda_) # Expected time in queue # Probabilities P0 = 1 - rho # Probability system empty Pn = lambda n: (1 - rho) * rho**n # Probability of n in system return { "model": "M/M/1", "arrival_rate": lambda_, "service_rate": mu, "utilization": rho, "L": L, "Lq": Lq, ...