A stochastic model consisting of two heterogeneous channels and having no waiting room in front of each is considered. A customer who has completed his service in channel 1 while channel 2 is busy blocks channel 1 with probability
Due to the recent developments in the fields of production line and communication, new queuing theory models are needed. In this sense, significant improvements in serial channel models have been observed. A tandem queueing system consist of two stage with waiting in each stage considered and joint limit distribution of waiting times of
In this study, we discuss a tandem model consisting of two stages channels: a stochastic queueing model consisting of two heterogeneous channels and having no waiting room in front of each is considered. A customer who has completed his service in channel 1 while channel 2 is busy blocks channel1 with probability
This model is defined as follows: a customer completes his service in channel 1 (when this channel is empty), enters into channel 2 (when channel two is empty), and leaves the system after receiving service. The customer, who has completed his service in channel 1, while channel 2 is busy, blocks channel 1 with probability
The tandem model with blocking.
Channel 1 can be empty, busy, or blocked. Let them be represented them with 0, 1, and
If we solve this steadystate equations, we obtain the
Since there is no queue in the system,
The
Equality (
Let
Considering
The simulation of queuing system requires keeping of event list to determine what will happen in the next step. Events in simulations occur at random times to imitate randomness in real life (we do not know precisely when a customer arrives or how long the service lasts). Obtaining randomness that is required to simulate real life is possible using “random numbers.” In the system, simulation results obtained from Matlab program for different probabilities of blocking channel 1 are given in tables below. Depending on various probabilities of blocking
Loss probabilities for
Number of 



 

Pr_{sim}  Pr_{exact}  Pr_{sim}  Pr_{exact}  Pr_{sim}  Pr_{exact}  Pr_{sim}  Pr_{exact}  
4000  0.749739  0.666667  0.621271  0.77551  0.605388  0.867925  0.597085  0.90991 
6000  0.749664  0.666667  0.636181  0.77551  0.621225  0.867925  0.613301  0.90991 
20000  0.749629  0.666667  0.740998  0.77551  0.731758  0.867925  0.726884  0.90991 
Loss probabilities for
Number of 



 

Pr_{sim}  Pr_{exact}  Pr_{sim}  Pr_{exact}  Pr_{sim}  Pr_{exact}  Pr_{sim}  Pr_{exact}  
4000  0.742478  0.666667  0.733363  0.71739  0.723433  0.765957  0.718256  0.78947 
6000  0.738897  0.666667  0.729511  0.71739  0.719331  0.765957  0.713901  0.78947 
20000  0.713914  0.666667  0.702537  0.71739  0.690275  0.765957  0.683827  0.78947 
Loss probabilities for
Number of 



 

Pr_{sim}  Pr_{exact}  Pr_{sim}  Pr_{exact}  Pr_{sim}  Pr_{exact}  Pr_{sim}  Pr_{exact}  
4000  0.701866  0.500000  0.692689  0.65094  0.682842  0.762295  0.677761  0.80769 
6000  0.695796  0.500000  0.687814  0.65094  0.679183  0.762295  0.674738  0.80769 
20000  0.653493  0.500000  0.653303  0.65094  0.653278  0.762295  0.653290  0.80769 
In the study, the loss probability of the customer in two heterogeneous channels tandem system was calculated. Additionally, optimal orders of channels were obtained. Theoretically, simulation study supported obtained system results. Exact and simulation results of the loss probability were given in Tables
Finally, much more study can be done on this topic of interest by increasing the number of channels in the system.