Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Computer Engineering and Sciences

First Advisor

Ivica Kostanic

Second Advisor

Susan Earles

Third Advisor

Carlos Otero

Fourth Advisor

Howell Heck


Public Safety organizations play a vital role in emergencies. Their ultimate goal is to protect people and save lives and properties during disasters. Public safety communities have been using narrowband Trunking systems for their communications for decades. These systems were designed with only voice communications in mind. Even though these narrowband systems have gone throughout many enhancement phases, yet their data capabilities are still limited. Long Term Evolution (LTE) has been selected by many countries including the United States to be the platform for next-generation Public Safety Networks(PSN). The 3GPP LTE standard is all-IP architecture mainly developed to boost its previous standards data capabilities. Its tremendous data capabilities can support not only Push-To-Talk but also Push-To-Multimedia. The review of the literature shows that there is a shortage of studying the impact of the application nature of operation on its Grade Of Service (GOS). This dissertation aims at developing a queue model by applying a mathematical method called Queueing Theory to evaluate the performance of a Push-To-Talk application over LTE networks. A proper queueing model for a Push-ToTalk over LTE air-interface is analyzed and implemented in MATLAB and SimEvents simulation. The results of the proposed mathematical model are compared with the simulation results for validation. The air-interface queue model considered the impact of the overflow traffic on the performance of the system. The overflow traffic is resulting in group-call requests failure retrial. Unlike the Erlang-B model, the study led to a state-dependent model and that the Loss Probability LP is a more appropriate performance measure than the Blocking Probability BP. The model shows a high level of accuracy between mathematical and simulation results for low congested systems. As the network becomes congested, the impact of the overflow traffic becomes more significant. The mathematical model has been further tuned to compensate for the negative impact of the overflow traffic in congested systems. Furthermore, long sessions timeout model is suggested and analyzed if immediate system upgrade is not an available option. This model help finding out an appropriate timeout period to maintain the desired system Grade of Service GOS.