id author title date pages extension mime words sentence flesch summary cache txt cana-730 B. Deepa Cost Analysis Approach-the \(M^x / M / 1\) Queues with Working Breakdowns and Interruptions 2024 17 .pdf application/pdf 5243 249 62 [2πœ†2𝛼𝑍(1 βˆ’ 𝐺(𝑍))𝐺′(𝑍) βˆ’ π›Όπœ†2(1 βˆ’ 𝐺(𝑍)))2 βˆ’ π›Ύπœ†π›Ό[(1 βˆ’ 𝐺(𝑍) βˆ’ 𝑍𝐺′(𝑍)]]𝑃1,0 Ξ”β€²(𝑍) = πœ†3(1 βˆ’ 𝐺(𝑍)))3 + (1 βˆ’ 𝐺(𝑍)))2[βˆ’3πœ†3𝑍𝐺′(𝑍) + πœ†2(πœ‡π‘ + 𝛼 + πœ‡ + 𝛾) + πœ†(π›Όπœ‡π‘ + πœ‡πœ‡π‘ + π›Ύπœ‡π‘ + 𝛾𝛼 + π›Ύπœ‡)] + 𝐺′(𝑍)πœ†π‘[βˆ’π›Ύπ›Ό βˆ’ π›Ύπœ‡ + π›Ύπœ‡ 𝑍 βˆ’ π›Ύπœ‡π‘ βˆ’ π›Όπœ‡π‘ βˆ’ πœ‡πœ‡π‘ + πœ‡πœ‡π‘ 𝑍 ] + π›Ύπœ‡π‘[𝛼 + πœ‡] Now letting Z=1 then the above equations can be rewritten as follows: 𝑃0(1) From figure16 it is evident that total cost function decreases first and then increases consequently the convex nature arises in the total cost function. cache/cana-730.pdf txt/cana-730.txt