A Method for Cross-Layer Analysis of Transmit Buffer Delays in Message Index Domain

In data transmission systems, quality-of-service constraints are commonly defined in the form of buffer overflow probability or delay violation probability at a transmitter buffer. Some of the studies that employ the large-deviation principle have taken the buffer overflow probability as the quality-of-service constraint and performed the associated analyses in the time domain. The delay violation probability has been investigated through the buffer overflow probability given that there exists a constant service rate from or a constant data arrival rate at a buffer. These studies cultivated the concepts of effective bandwidth and effective capacity, respectively. Different from the existing studies, we investigate the performance of a transmitter buffer in the message index domain rather than the time domain by taking the waiting time (buffering delay) as the primary quality-of-service constraint. We characterize the waiting time violation probability when both the data arrival and service processes are stochastic, and provide two new concepts: effective interarrival time and effective service time, which are the duals of effective bandwidth and effective capacity, respectively, in the message index domain. The effective interarrival time of a data arrival process determines the maximum constant service time for a message that can sustain the arrival process under a stochastic waiting time constraint, and the effective service time of a data service process determines the minimum constant interarrival time between successive messages arriving at a buffer that the service process can sustain. We show that we can obtain the effective capacity of a service process or the effective bandwidth of an arrival process through the effective service time or the effective interarrival time of the corresponding process, respectively, in cases where it is difficult to formulate the effective capacity and the effective bandwidth without numerical techniques or particular assumptions. Noting that our proposed techniques can be applied in vehicular communication scenarios, e.g., highways, urban areas, and rural areas, we finally analyze a typical data dissemination and collection task in vehicular networks using a broadcast downlink and a slotted Aloha uplink transmission.