A controller for generating a target operational speed band (53; 63; 67) for a host vehicle travelling along a route, the controller comprising: processing means for receiving an input to identify a first time-dependent obstacle at a first location on the route, the first time-dependent obstacle being identified as hindering progress of the host vehicle during a first time period; and memory means connected to the processing means ; wherein the processing means is configured to: define the first time-dependent obstacle in a two-dimensional speed against distance map ; determine a first speed trajectory (51, 52; 61; 65, 66) from a first point to a second point within the two-dimensional speed against distance map , the second point representing the first location on the route and the determined first speed trajectory (51, 52; 61; 65, 66) representing the host vehicle arriving at the first location at a first arrival time, the first arrival time being outside the first time period; and generate the target operational speed band (53; 63; 67); wherein the first speed trajectory (51, 52; 61; 65, 66) forms one of an upper limit and a lower limit of the target operational speed band (53; 63; 67), and the first speed trajectory (51, 52; 61; 65, 66) is generated for a first acceleration limit of the host vehicle . processing means for receiving an input to identify a first time-dependent obstacle at a first location on the route, the first time-dependent obstacle being identified as hindering progress of the host vehicle during a first time period; and memory means connected to the processing means ; wherein the processing means is configured to: define the first time-dependent obstacle in a two-dimensional speed against distance map ; determine a first speed trajectory (51, 52; 61; 65, 66) from a first point to a second point within the two-dimensional speed against distance map , the second point representing the first location on the route and the determined first speed trajectory (51, 52; 61; 65, 66) representing the host vehicle arriving at the first location at a first arrival time, the first arrival time being outside the first time period; and generate the target operational speed band (53; 63; 67); wherein the first speed trajectory (51, 52; 61; 65, 66) forms one of an upper limit and a lower limit of the target operational speed band (53; 63; 67), and the first speed trajectory (51, 52; 61; 65, 66) is generated for a first acceleration limit of the host vehicle . define the first time-dependent obstacle in a two-dimensional speed against distance map ; determine a first speed trajectory (51, 52; 61; 65, 66) from a first point to a second point within the two-dimensional speed against distance map , the second point representing the first location on the route and the determined first speed trajectory (51, 52; 61; 65, 66) representing the host vehicle arriving at the first location at a first arrival time, the first arrival time being outside the first time period; and generate the target operational speed band (53; 63; 67); wherein the first speed trajectory (51, 52; 61; 65, 66) forms one of an upper limit and a lower limit of the target operational speed band (53; 63; 67), and the first speed trajectory (51, 52; 61; 65, 66) is generated for a first acceleration limit of the host vehicle . <EOS>