SJC Controller described a taxi conflict event resulting in an abrupt stop by one of the aircraft; the reporter acknowledging more positive sequencing instructions should have been issued prior to the aircraft taxiing.

Narrative

Air Carrier Y called ready for taxi to Runway 30R. I instructed the aircraft to taxi via Taxiways Z; H; Y to Runway 30R. Immediately after; Air Carrier X called for taxi. I instructed that aircraft to taxi via Taxiways Z; G; Y to Runway 30R. As Air Carrier Y was making his turn from H to Y; Air Carrier X was starting his turn from Z onto G further down field. When Air Carrier Y became established on Y and saw Air Carrier X ahead of him; the pilot sped the aircraft's taxi speed up to pass the other aircraft. Air Carrier X had to come to an abrupt halt on G to allow Air Carrier Y to pass. I had instructed neither aircraft to pass behind the other. As Air Carrier X reached the end of Y; the pilot reported that the previous abrupt halt had caused a cabin incident. I should have instructed one of the aircraft to pass behind the other to insure positive control on the taxiways. In this case; the sequence should have been the Air Carrier Y first and Air Carrier X second. This instruction should have been given when Air Carrier X initially called ready for taxi.