Summary: We address the problem of assigning probabilities at discrete time instants for routing toll-free calls to a given set of call centers to minimize a weighted sum of transmission costs and load variability at the call centers during the next time interval. We model the problem as a tripartite graph and decompose the finding of an optimal probability assignment in the graph into the following problems: (i) estimating the true arrival rates at the nodes for the last time period; (ii) computing routing probabilities assuming that the estimates are correct. We use a simple approach for arrival rate estimation and solve the routing probability assignment by formulating it as a convex quadratic program and using the affine scaling algorithm to obtain an optimal solution. We further address a practical variant of the problem that involves changing routing probabilities associated with \(k\) nodes in the graph, where \(k\) is a prespecified number, to minimize the objective function. This involves deciding which \(k\) nodes to select for changing probabilities and determining the optimal value of the probabilities. We solve this problem using a heuristic that ranks all subsets of \(k\) nodes using gradient information around a given probability assignment. The routing model and the heuristic are evaluated for speed of computation of optimal probabilities and load balancing performance using a Monte Carlo simulation. Empirical results for load balancing are presented for a tripartite graph with 99 nodes and 17 call center gates.