Development of partial ring, dedicated breast positron emission tomography (PET) scanners is an active area of research. Due to the limited angular coverage, generation of distortion and artifact-free, fully 3D tomographic images is not possible without rotation of the detectors. With time-of-flight (TOF) information, it is possible to achieve the 3D tomographic images with limited angular coverage and without detector rotation. We performed simulations for a breast scanner design with a ring diameter and an axial length of 15 cm and comprising a full (180 degrees in-plane angular coverage), 2/3 (120 degrees in-plane angular coverage) or 1/2 (90 degrees in-plane angular coverage) ring detector. Our results show that as the angular coverage decreases, improved timing resolution is needed to achieve distortion-free and artifact-free images with TOF. The contrast recovery coefficient (CRC) value for small hot lesions in a partial ring scanner is similar to a full ring non-TOF scanner. Our results indicate that a timing resolution of 600 ps is needed for a 2/3 ring scanner, while a timing resolution of 300 ps is needed for a 1/2 ring scanner. We also analyzed the ratio of lesion CRC to the background pixel noise (SNR) and concluded that TOF improves the SNR values of the partial ring scanner, and helps to compensate for the loss in sensitivity due to reduced geometric sensitivity in a limited angle coverage PET scanner. In particular, it is possible to maintain similar SNR characteristic in a 2/3 ring scanner with a timing resolution of 300 ps as in a full ring non-TOF scanner.