The problems of analysis and synthesis of the response system to emergency situations in difficult cases are shown here. The response system is considered as a queuing system of applications of several types requiring the use of one, two or more channels (for example mobile fire-rescue units, ambulance brigades, police and medical care). The relevance of this problem is caused by the presence of autonomous objects in an environment where the number of mobile emergency response units of the system is limited. The analysis problem is formulated as finding the probability of system failure in the reception of applications (of the 1st type pI, the 2nd type pII and 3rd type pIII) for a given number of service channels n , when the intensities {λ} and {μ} are known, which are the parameters of exponential distribution laws. The synthesis problem is formulated as finding the required number of service channels n under certain intensities {λ} and {μ} and set limits on allowable probability of failure pI- pIII. Analytical expressions for the probabilities of system states through the given loads are obtained for the two types of applications of the service system α1 = λ1/μ1 and α2 = λ2/μ2, presented in table form. The general expressions for the probability of unoccupied n channels are also obtained - p0 and failure probability - pI and pII, which can be used for analysis of n -channel queuing system of this type. The nomogram with lines of equal values of n in the coordinates is encouraged to use to solve the problem of synthesis of these systems (α1, α2). For this purpose the dependences α2 = f (α1, n ) are obtained, and they are found in the form of polynomials, whose coefficients depend on the given load α1, the number of service channels n and the probability of failure in the admission of an application. Formula to determine these coefficients and to determine the given load α2 is obtained. It was found that the two types of applications service system for odd values of n at least one service channel may always remain free. Analytical solutions for the evaluation of the probability of states of this queuing system are obtained for the application service system of three types. The examples show the possibility of solving problems of analysis and synthesis of queuing systems with heterogeneous applications using nomograms. This study is a logical continuation of the previously published article “Modeling of sufficiency of the mobile emergency units in case of situations of high complexity.