The　emergence　of　connected　vehicle　(CV)　technologies　has　created　new　traffic　control　opportunities,　among　them,　is　the　potential　to　estimate　volume　without　approach　lane　detection.　Rather　than　requiring　the　expense　and　effort　to　install　and　maintain　detector　systems,　this　new　``detector-free＇＇　method　permits　traffic　volume　to　be　estimated　from　CV　GPS　trajectory　data.　Unfortunately,　however,　CV　GPS　methods　are　limited　not　only　to　locations　where　CV　GPS　data　can　be　recorded,　but　also　limited　to　time　when　CV　GPS　data　is　recorded.　The　goal　of　this　research　was　to　overcome　these　limitations　and　permit　volume　estimation　to　be　accomplished　under　any　location　or　condition,　including　low-penetration　CV　environments.　The　contributions　made　by　this　work　are　significant　in　two　respects.　First,　it　creates　an　improved　queue-based　method　to　estimate　intersection　approach　volumes　during　each　signal　cycle　with　sparse　CV　data.　Second,　the　research　demonstrates　the　application　of　a　Bayesian　deduction　method　to　approximate　volume　with　no　CV　trajectory　data.　To　accomplish　this,　traffic　volumes　are　assumed　to　be　time-dependent　Poisson　distributed　throughout　the　day,　and　CV　data　were　used　to　estimate　CV　volume　and　further　set　as　prior　to　deduce　the　time-dependent　Poisson　arrival　rate.　To　verify　and　evaluate　the　accuracy　and　effectiveness　of　this　new　method　under　a　range　of　potential　traffic　conditions,　a　simulation　case　study　and　a　NGSIM　case　study　were　implemented.　Results　of　both　case　studies　resulted　in　estimated-to-actual　arrival　rate　average　errors　as　low　as　4.2　percent　and　volume　estimation　errors　as　low　as　0.9　percent.