One of the fundamental problems in many-pixel detectors implemented in cryogenics environments is the number of bias and read-out wires. If one targets a megapixel range detector, number of wires should be significantly reduced. One possibility is that the detectors are serially connected and biased by using only one line and read-out is accomplished by on-chip circuitry. In addition to the number of pixels, the detectors should have fast response times, low dead times, high sensitivities, low inter-pixel crosstalk and ability to respond to simultaneous irradiations to individual pixels for practical purposes. We have developed an equivalent circuit model for a serially connected superconducting strip line detector (SSLD) array together with the read-out electronics. In the model we take into account the capacitive effects due to the ground plane under the detector, effects of the shunt resistors fabricated under the SSLD layer, low pass filters placed between the individual pixels that enable individual operation of each pixel and series resistors that prevents the DC bias current flowing to the read-out electronics as well as adjust the time constants of the inductive SSLD loop. We explain the results of investigation of the following parameters: Crosstalk between the neighbor pixels, response to simultaneous irradiation, dead times, L/R time constants, low pass filters, and integration with the SFQ front-end circuit. Based on the simulation results, we show that SSLDs are promising devices for detecting a wide range of incident radiation such as neurons, X-rays and THz waves in many-pixel configurations.