The rapid growth of computer‐communication services means that telephone‐conversation traffic must compete for system resources with computer‐communication traffic carried by dial‐up connections to the Internet or intranets over public telephone switching networks. The traffic characteristics differ for the two types of service; for example, the mean holding time and peak traffic periods are different. However, because dial‐up connection calls occupy circuit lines for a long time, the grade of service (GoS) of telephone‐conversation calls may deteriorate during periods of peak demand. Another problem is that since a telephone switching network is dimensioned to satisfy the required GoS for telephone calls during peak demand periods, there will be surplus resources, and a significant opportunity cost, during off‐peak periods. One way to efficiently use these surplus switching‐network resources is to offer fixed‐cost best‐effort dial‐up connection service during off‐peak periods for telephone traffic. This also makes the demand for dial‐up connections less likely to affect the GoS of telephone‐conversation calls during peak periods. We propose a priority control scheme for such an off‐peak service. This scheme works as follows in a telephone switching system where both high‐priority telephone‐conversation calls and low‐priority dial‐up connection calls are offered. When a call arrives at the system and there are adequate resources available for an ordinary telephone‐conversation call, a high‐priority telephone call or a low‐priority dial‐up connection call can be connected. However, if a high‐priority call arrives at the system and there are not enough resources available to allow connection, an already connected dial‐up connection call is forcibly cut off to enable connection of the high‐priority telephone call, and thus guarantee the GoS of telephone calls. We evaluate the performance of a telecommunication system based on this scheme by using a Markov model. We derive the call‐blocking probabilities for both call types and the ratio of the amount of traffic that is forcibly cut off to the amount of offered traffic in the system, and show calculated results. We also discuss some guidelines for offering services using this scheme. © 2000 Scripta Technica, Electron Comm Jpn Pt 1, 83(6): 78–87, 2000