BE35 pilot reported fuel starvation in the traffic pattern and a successful engine out landing.

Narrative

Running out of fuel in the main tank in the traffic pattern of the destination airport. Due to the low altitude; the decision was made to execute an engine out landing on the available runway and not to troubleshoot the engine or the fuel management. The landing was successfully performed with no damage to/impact on the aircraft. It was later determined that the engine monitor reads the tank level incorrectly. It is also suspected that the fuel burn reported by the monitor is not given correctly (under investigation). The aircraft has several tanks that separately do not hold a lot of fuel. The pilot had little experience in type and in the particular aircraft flown. All variables let the pilot believe that there is enough fuel plus reserve to make an uneventful landing.In airplanes with 'complex' fuel management and limited experience of the pilot in type and plane; extra caution and reserves should be considered when it comes to the fuel management. For future flights; the pilot will switch away from the left main tank as soon as practicable and burn all other available fuel; to make sure that there are most fuel reserves available in the left main for the approach and landing. This will be particularly important for potential IMC situations; where a missed approach and reattempt landing have to be considered.