SessionStorage is per tab/window, so you can define a random number in sessionStorage and get it at first if exists:
var tabID = sessionStorage.tabID ?
sessionStorage.tabID :
sessionStorage.tabID = Math.random();
UPDATE:
In some cases, you may have same sessionStorage in multiple tab (e.g. when you duplicate tab). In that case, following code may help:
var tabID = sessionStorage.tabID &&
sessionStorage.closedLastTab !== '2' ?
sessionStorage.tabID :
sessionStorage.tabID = Math.random();
sessionStorage.closedLastTab = '2';
$(window).on('unload beforeunload', function() {
sessionStorage.closedLastTab = '1';
});