# Throughput of Buffer with Dependent Service Times
## 7 Conclusions  
We studied the throughput and losses of a buffer whose service times are stochastically dependent. We derived formulae for the count of packets processed and lost in an arbitrary period, the temporary output traffic intensity, the temporary intensity of packet losses, \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(\mathbf{C=1}\) & \(\mathbf{C=2}\) & \(\mathbf{C=3}\) & \(\mathbf{C=4}\) \\ \hline \(\rho_{1}=0.1\) & 89.2/89.1 & 85.8/85.7 & 79.4/79.3 & 69.7/69.6 \\ \hline \(\rho_{1}=0.2\) & 78.0/78.0 & 76.1/76.1 & 72.8/72.6 & 66.4/66.4 \\ \hline \(\rho_{1}=0.3\) & 68.9/69.0 & 68.3/68.2 & 67.1/67.1 & 63.6/63.5 \\ \hline \(\rho_{1}=0.4\) & 65.5/65.5 & 65.3/65.4 & 64.9/65.1 & 62.4/62.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Theoretical versus simulated throughput for various combinations of \(\rho_{1}\) and \(C\) (theoretical \(T\)/simulated \(T\)). \(K=20\), traffic intensity = 1. Figure 17: Stationary throughput \(T\) versus buffer size \(K\), for four different values of traffic intensity. \(C=4\) and \(\rho_{1}=0.2\). buffer throughput, and loss probability. Analytical findings were accompanied by numeric calculations that demonstrated the influence of the correlation coefficient of consecutive service times, the standard deviation of the interval between packets, and initial buffer occupancy on the throughput and related characteristics. Theoretical results were confirmed in discrete-event simulations. Future work can focus on two directions. Firstly, other important characteristics of the same model can be investigated. For instance, to the best of the author's knowledge, the time-dependent workload of the system has not been explored so far. Secondly, the model itself can be further modified and expanded to include, e.g., a group arrival process, a group service process, etc., and then studied with respect to time-dependent characteristics. This research received no external funding. Data Availability Statement: Data is contained within the article. The author declares no conflict of interest. * _[PERSON] et al. (2012)_ [PERSON]; [PERSON], [PERSON]; [PERSON] Analytically explicit results for the GI/C-MSP/1/\(\infty\) queueing system using roots. _Probab. Eng. Inf. Sci._**2012**, _26_, 221-244. [CrossRef]
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