MAXBAND : a versatile program for setting signals on arteries and triangular networks

MAXBAN) is a portable, off-line, FORTRAN IV computer program for setting arterial signals to achieve maximal bandwidth. Special features of the program include (1) automatically choosing cycle time from a given range, (2) permitting the design speed to vary within given tolerances, (3) selecting the best lead or lag pattern for left turn phases from a specified set, (4) allowing a queue clearance time for secondary flow accumulated during red, (5) accepting user-specified weights for the green bands in each direction; and (6).handling a simple network in the form of a three artery triangular loop. Green splits can be provided or, alternatively, flows and capacities given and splits calculated using Webster's theory. The program produces cycle time, offsets, speeds, and order of left turn phases to maximize the weighted combination of bandwidths. The optimization employs Land and Powell's MPCODE branch and bound algorithm. Up to 12 signals can be handled efficiently. The MAXBAND program is available from the Federal Highway Administration. Signal setting methods for fixeC-time systems separate broadly into two classes. The first, and historically oldest, consists of methods that maximize bandwidth and progression. This grcup includes, among others, Little and Morgan (1964), Little (1966) and Messer, Wv4hitson, Dudek, and Romano (1974). The second group contains methods that seek to minimize delay, stops or other measures of disutility. Examples are the combination method (Hillier 1966), SIGOP. (Traffic Research Corporation 1966), TRANSYT (Robertson 1969), MITROP (Gartner, Little, and Gabbay 1975) and SIGOP II (Lieberman and Woo 1976). Although disutility-oriented methods have now been available for some time, many traffic engineers continue to prefer maximal bandwidth settings because they have certain inherent advantages. For one thing, bandwidth methods use relatively little input, the basic requirements being street geometry, traffic speeds, and green splits. Secondly, progression systems are operadonaily robust. Space time diagrams let the traffic engineer visualize easily the quality of the results. Through accumulated experience, engineers with knowledge of the specific streets can spot problems and, if necessary, make modifications to the settings. In addition, various studies (e.g., Wagner, Gerlough and Barnes (1969)) and much practical experience have shown that bandwid:h systems give good results in the field. It may even be that drivers expect sic-al progression and take it as a measure of setting.quality. In any case, we take the position here that, if engineers are going to use bandwidth systems, they should have the best. Morgan and Little (1964) first computerized the setting of arterial signals for maximal bandwidth. The widely distributed program of Little, Martin and Morgan (1966) efficiently finds offsets for maximal bandwidth given cycle time, red times, signal distances and street speed. The total bandwidth attained can be allocated between directions on the basis of flow. Little (1966) subsequently generalized the co= utation in several ways: The cycle time could be automatically selected from a given range and so could speed. Networks could be solved. These and several further extensions became possible through a mixed-integer formulation of the problem. The flexibility thereby introduced has several advantages. For example, maximal bandwidth calculations frequently have adisconcerting feature. On a long street the signals that constrict bandwidth may turn out to be far apart. A small change in desisg speed or cycle time can