Round robin and its variants are well known scheduling policies that are popular in wireline networks due to their throughput optimality, delay insensitivity to file size distributions and short-term fairness. The latter two properties are also extremely important for emerging wireless applications, such as Internet of Things and cyber-physical systems. However, there is no direct wireless analog of round robin with all the desirable properties in wireless networks, where wireless interference and channel fading are predominant. The main reason is due to the fact that it is very difficult to even define what round robin means in wireless networks. This motivates us to develop a round-robin-like algorithm in wireless networks that has nice properties as round robin in wireline networks. To that end, we utilize a counter called the Time-Since-Last-Service (TSLS) that keeps track of the time of each file since its last service, and observe that scheduling a file with maximum TSLS in a single server is equivalent to serving files in a round robin fashion. Based on this key observation, we develop a TSLS-based algorithm that balances the tradeoff between the TSLS value and the channel rate for each link and show that the proposed algorithm achieves maximum system throughput, which demands a nontraditional approach due to the abrupt dynamics of the TSLS metrics. Numerous simulations are provided to validate its desired properties such as delay insensitivity and excellent short-term fairness performance as in the case of round robin algorithms of wireline networks.